Economic Analysis of 4G Network Upgrade

Save this PDF as:
 WORD  PNG  TXT  JPG

Size: px
Start display at page:

Download "Economic Analysis of 4G Network Upgrade"

Transcription

1 Economic Analysis of ework Upgrade Lingjie Duan, Jianwei Huang, and Jean Walrand Absrac As he successor o he sandard, provides much higher daa raes o address cellular users ever-increasing demands for high-speed mulimedia communicaions. This paper analyzes he cellular operaors iming of nework upgrades and models ha users can swich operaors and services. Being he firs o upgrade o service, an operaor increases his marke share bu akes more risk or upgrade cos because echnology maures over ime. This paper firs sudies a monopoly marke wih one dominan operaor and some small operaors, where he monopolis decides his upgrade ime by rading off increased marke share and upgrade cos. The paper also considers a compeiion marke and develops a game heoreic model for sudying operaors ineracions. The analysis shows ha operaors selec differen upgrade imes o avoid severe compeiion. One operaor akes he lead o upgrade, using he benefi of a larger marke share o compensae for he larger cos of an early upgrade. This resul maches well wih many indusry observaions of asymmeric upgrades. The paper furher shows ha he availabiliy of upgrade may decrease boh operaors profis due o increased compeiion. Perhaps surprisingly, he profis can increase wih he upgrade cos. I. ITRODUCTIO The hird generaion of cellular wireless neworks was launched during he las decade. I has provided users wih high-qualiy voice channels and moderae daa raes up o Mbps. However, service canno seamlessly inegrae he exising wireless echnologies e.g., GSM, wireless LA, and Blueooh [], and canno saisfy users fas growing needs for high daa raes. Thus, mos major cellular operaors worldwide plan o deploy he fourh-generaion neworks o provide much higher daa raes up o hundreds of megabis per second and inegrae heerogeneous wireless echnologies. The echnology is expeced o suppor new services such as high-qualiy video cha and video conferencing [3]. One may expec compeiive operaors in he same cellular marke o upgrade o a service a abou he same ime. However, many indusry examples show ha symmeric upgrades do no happen in pracice, even when muliple op- L. Duan is wih he Engineering Sysems and Design Pillar, Singapore Universiy of Technology and Design J. Huang is wih he ework Communicaions and Economics Lab, Deparmen of Informaion Engineering, The Chinese Universiy of Hong Kong J. Walrand is wih he Deparmen of Elecrical Engineering and Compuer Sciences, Universiy of California a Berkeley, California This work is suppored by SUTD-MIT Inernaional Design Cener Gran Projec no.: IDSF6OH and SUTD Sar-up Research Gran Projec no.: SRG ESD 4. This work is also suppored by he General Research Funds Projec umber CUHK 47 and CUHK 45 esablished under he Universiy Gran Commiee of he Hong Kong Special Adminisraive Region, China, and he SF-eSE grans 438 and 97. eraors have obained he necessary specrum and echnology paens for upgrade [3], [4]. In Souh Korea, for example, Korean Telecom ook he lead o deploy he world s firs nework using WiMAX echnology in 6, whereas SK Telecom sared o upgrade using more maure LTE echnology in. In US, Sprin deployed he firs WiMAX nework in lae 8, Verizon waied unil he end of o deploy his LTE nework, and AT&T planed o deploy his LTE nework a he end of [3]. In China, China Mobile and China Unicom are he wo dominan cellular operaors, and China Mobile has decided o firs deploy LTE nework during -3 [4]. Thus, he key quesion we wan o answer in his paper is he following: How do he cellular operaors decide he iming o upgrade o neworks? In his paper, we analyze he iming of operaors upgrades in differen models, including boh a monopoly marke and a compeiion marke. Operaors need o pay he cos of upgrade, which decreases over ime as echnology maures. There are wo key facors ha affec he operaors upgrade decisions: namely, upgrade cos and user swiching cos. An exising user can swich o he service of he same operaor or of a differen operaor, depending on how large he swiching cos is. In a monopoly marke where only a dominan operaor can choose o upgrade o, his operaor can use he service o capure a larger marke share from small operaors. In a compeiion marke where muliple operaors can choose o upgrade, we analyze he operaors ineracions as a non-cooperaive game. We sudy how he users iner-nework swiching cos affecs he operaors upgrade decisions, and our findings are consisen wih he asymmeric upgrades observed in he indusry. Our key resuls and conribuions are as follows. A revenue-sharing model beween operaors: Mos exising works only sudy a single nework s revenue by exploring he nework effec e.g., [7], and he resuls may no apply in a compeiive marke. In Secion III, we sudy wo inerconneced neworks, where heir operaors share he revenue of he iner-nework raffic. Monopolis s opimal iming of upgrade: By upgrading early, he monopolis in Secion IV obains a large marke share and a large revenue because of s Qualiy of Service QoS improvemen, bu i canno benefi from he cos depreciaion over ime. When he upgrade cos is relaively low, he upgrades a he earlies available ime; oherwise he pospones his upgrade. Compeiive operaors asymmeric upgrades: In Secions V and VI, users can swich operaors. By upgrading early, an operaor capures a large marke share and

2 he s QoS improvemen which can compensae for he large upgrade cos. The oher operaor, however, pospones his upgrade o avoid severe compeiion and benefis from cos reducion. The availabiliy of upgrade may decrease boh operaors profis because of he increased compeiion, and paradoxically, heir profis may increase wih he upgrade cos. II. RELATED WORK A. ework Effec and ework Value In elecommunicaions, he nework effec is he added value ha a user derives from he presence of oher users [3]. In a nework wih users, each user perceives a value ha increases wih. A reasonable model was suggesed by Briscoe e al. [7], where each user perceives a value of order log. In ha model, a user ranks he oher users in decreasing order of imporance and assigns a value /k o he k-h user in ha order, for a oal value +/+ +/ log. The resuling oal nework value is log, which is appropriae for cellular neworks shown by quaniaive sudies [7]. B. ework Upgrade Recenly, here has been a growing ineres in sudying he economics of nework upgrades [8] []. Musacchio e al. [8] sudied he upgrade iming game beween wo inerconneced Inerne Service Providers ISPs, where one ISP s archiecure upgrade also benefis he oher because of he nework effec. This free-riding effec may make he second operaor pospone his upgrade or even never decide o upgrade. Jiang e al. [9] sudied a nework securiy game, where one user s invesmen upgrade can reduce he propagaion of compuer viruses o all users. In our problem, however, one operaor may benefi from he oher s upgrade only when he also upgrades, leing his users communicae wih exising users in oher neworks. Moreover, our model characerizes he dynamics of users swiching beween operaors and/or services. These dynamics imply ha an operaor can obain a larger marke share by upgrading earlier, and his weakens he free-riding effec. Sen e al. [] sudied he users adopion and diffusion of a new nework echnology in he presence of an incumben echnology. Our work is differen from ha sudy in ha we are no focusing on echnology compeiion o arac users, bu on he operaors compeiion in upgrade iming o obain greaer profis. Moreover, he swiching cos is no considered in [], whereas i is an imporan parameer of our model. A. Value of Cellular eworks III. SYSTEM MODEL In his paper, we adop he log Law, where he nework value wih users is proporional o log. The operaor of a cellular nework prefers a large nework value; his is because he revenue he obains by charging users can be proporional o he nework value. oice ha he value of a nework is larger han a nework even when wo neworks have he same number of users. This is because he communicaion beween wo users is more efficien and more frequen han beween wo users. Because he average daa rae in he service is 5- imes faser han he boh downlink and uplink, a nework can suppor many new applicaions. We denoe he efficiency raio beween and services as γ,. Tha is, by serving all his users via QoS-guaraneed raher han services, an operaor obains a larger normalized revenue log insead of γ log. oe ha his resul holds for a single operaor s nework ha is no conneced o oher neworks. ex we discuss he revenues of muliple operaors whose neworks e.g., wo neworks are inerconneced. For he purpose of illusraion, we consider wo neworks ha conain and users, respecively. The whole marke covers = + users. We assume ha wo operaors and laer services are equally good o users, and he efficiency raio γ is he same for boh operaors. The raffic beween wo users can be inra-nework when boh users belong o he same operaor or iner-nework when wo users belong o differen operaors, and he revenue calculaions in he wo cases are differen. We assume ha he user who originaes he communicaion session irrespecive of wheher he same nework or o he oher nework pays for he communicaion. This is moivaed by he indusry observaions in EU and many Asian counries. Before analyzing each operaor s revenue, we firs inroduce wo pracical conceps in cellular marke: erminaion rae and user ignorance. When wo users of he same operaor communicae wih each oher, he calling user only pays operaor. Bu when an operaor s user calls an operaor s user, operaor charges a erminaion rae for he incoming call []. 3 We denoe he wo operaors revenue-sharing porion per iner-nework call as η, where he value of η, depends on he agreemen beween he wo operaors or on governmens regulaion on erminaion rae. User ignorance is a unique problem in he wireless cellular nework, where users are ofen no able o idenify which specific nework hey are calling. Mobile number porabiliy furher exacerbaes his problem [4]. Thus a ypical user s evaluaion of wo inerconneced neworks does no depend on which nework he belongs o, and equals γ log where = +. We assume a call from any user erminaes a a user in nework i {, } wih a probabiliy of i / as in [4]. The operaors revenues when hey are boh providing services are given in Lemma. Lemma : When operaors and provide services, heir revenues are γ log and γ log, respecively. The proof of Lemma is given in our online echnical repor We assume ha an operaor s operaional cos proporional o nework value has been deduced already, and hus he revenue in his paper represens a normalized one. Our model can also be exended o he case where boh involved users in a communicaion session pay for heir communicaion. This is wha happening in US cellular marke. 3 In he US, erminaion rae follows Bill and Keep and is low. Then operaor can keep mos of he calling user s paymen. In EU, however, erminaion rae follows Calling Pary Pays and is much higher. Then mos of he calling user s paymen o operaor is used o compensae for he erminaion rae charged by operaor [].

3 []. Boh operaors revenues are linear in heir numbers of users or marke share, and are independen of he sharing porion η of he iner-nework revenue. Inuiively, he inernework raffic beween wo neworks is bidirecional: when a user originaes a call from nework o anoher user in nework, his iner-nework raffic generaes a fracion η of corresponding revenue o operaor ; when he oher user calls back from nework o nework, he generaes a fracion η of he same amoun of revenue o operaor. Thus an operaor s oal revenue is independen of η. Laer, in Secion IV, we show ha such independence on η also applies when he wo operaors boh provide services or provide mixed and services. B. User Churn during Upgrade from o Services When service becomes available in he marke offered by one or boh neworks, he exising users have an incenive o swich o he new service o experience a beer QoS. Such user churn does no happen simulaneously for all users, his is because differen users have differen sensiiviies o qualiy improvemens and swiching coss []. We use wo parameers λ and α o model he user churn wihin and beween operaors: Inra-nework user churn: If an operaor provides in addiion o his exising service, his users need o buy new mobile phones o use he service. The users also spend ime o learn how o use he service on heir new phones. We use λ o denoe he users swiching rae o he service wihin he same nework. Iner-nework user churn: If a user wans o swich o anoher nework s service, he eiher wais ill his curren conrac expires, or pays for he penaly of immediae conrac erminaion. This means ha inernework user churn incurs an addiional cos on op of he mobile device updae, and hus he swiching rae will be smaller han he inra-nework user churn. We use αλ o denoe he users iner-nework swiching rae o service, where α, reflecs he ransacion cos of swiching operaors. We illusrae he process of user churn hrough a coninuous ime model. The saring ime = denoes he ime when he specrum resource and he echnology are available for a leas one operaor see Secion IV for monopoly marke and Secion VI for compeiion marke. We also assume ha he porion of users swiching o he service follows he exponenial disribuion a rae λ for inra-nework churn and αλ for iner-nework churn. As an example, assume ha operaor inroduces a service a ime = T while operaor decides no o upgrade. The numbers of operaor s users and users a any ime are and, respecively. The number of operaor s users a ime is. As ime increases from T, users in boh neworks sar o churn o service, and = e λ max T,, = e αλ max T,, Operaor s users: Operaor s users: T Operaor s users: Fig.. The numbers of users in he operaors differen services as funcions of ime. Here, operaor upgrades a T and operaor does no upgrade. and operaor s service gains an increasing marke share, = e λ max T, e αλ max T,. We illusrae and in Fig.. We can see ha operaor s early upgrade aracs users from his compeior and increases his marke share. oice ha increases wih α, hus operaor capures a large marke share when α is large i.e., he swiching cos is low. C. Operaors Revenues and Upgrade Coss Because of he ime discoun, an operaor values he curren revenue more han he same amoun of revenue in he fuure. We denoe he discoun rae over ime as S, and he discoun facor is hus e S a ime according o [6]. We approximae one operaor s upgrade cos as a oneime invesmen. This is a pracical approximaion, as an operaor s iniial invesmen of wireless specrum and infrasrucure can be much higher han he mainenance coss in he fuure. For example, specrum is a very scarce resource ha is allocaed aucioned infrequenly by governmen agencies. Thus an operaor canno obain addiional specrum frequenly afer his upgrade. To ensure a good iniial coverage, an operaor also needs o updae many base saions o cover a leas a whole ciy all a once. Oherwise, users would be unhappy wih he service, and his would damage he operaor s repuaion. Tha is why Sprin and Verizon covered many markes in heir iniial launch of heir services [8]. More specifically, we denoe he upgrade cos a = as K, which discouns over ime a a rae U. Thus if an operaor upgrades a ime, he needs o pay an upgrade cos Ke U according o [6]. We should poin ou ha he upgrade cos decreases faser han he normal discoun rae i.e., U > S. This happens because he upgrade cos decreases because of boh echnology improvemen and ime discoun. Very ofen he advance of echnology is he dominan facor in deermining U, and his is discussed furher in Secion VI. Based on hese discussions on revenue and upgrade cos, we define an operaor s profi as he difference beween his revenue in he long run and he one-ime upgrade cos. Wihou loss of generaliy, we will normalize an operaor s revenue rae a any ime, oal revenue, and upgrade cos by log, where is he oal number of users in he marke. 4 4 Our model and analyical resuls laer can be exended o he case where increases over ime. As new users prefer service o service, and can easily swich a rae λ, operaors will have more incenives o upgrade earlier.

4 IV. MOOPOLY MARKET We firs look a he case where only operaor can choose o upgrade from o, while he oher operaors one or more always offer he service because of he lack of financial resources or he necessary echnology. This can be a reasonable model, for example, for counries such as Mexico and some Lain American ones, where America Movil is he dominan cellular operaor in he marke. As he world s fourh-larges cellular nework operaor, America Movil has he advanage over oher small local operaors in winning addiional specrum via aucions and obaining LTE paens, and he is expeced o be he monopolis in ha area [5]. The key quesion in his secion is how operaor should choose his upgrade ime T from he service o he service. T = means ha operaor upgrades a he earlies ime ha he specrum and echnology are available, and T > means ha operaor chooses o upgrade laer o ake advanage of he reducion in he upgrade cos. Because of user churn from he o he service, he operaors marke shares and revenue raes change afer ime T. For ha reason, we analyze periods T and > T separaely. Before upgrade T : Operaor s and oher operaors marke shares do no change over ime. Operaor s revenue rae a ime is π = γ, which is independen of ime. His revenue during his ime period is π, T = T π e S d = γ S e ST. 3 Afer upgrade > T : Operaor s marke share increases over ime, and he oher operaors oal marke share denoed by / decreases over ime. We denoe operaor s numbers of users and users as and, respecively, and we have + + =. This implies ha = e αλ T, = e λ T, and = e λ T e αλ T. oe ha a user s communicaion wih a or a user is sill based on he sandard, and only he communicaion beween wo users can achieve a high sandard QoS. Operaor s revenue rae is γ π = + + γ γ, + which is independen of he revenue sharing raio η beween he calling pary and receiving pary. Operaor s revenue during his ime period is hen π,>t = T π e S d, 4 where is an approximaion of he long-erm service provision e.g., one decade before he emergence of he nex generaion sandard. This approximaion is reasonable since he revenue in he disan fuure becomes less imporan because of discoun. Figure illusraes how he numbers of users of operaors differen services change over ime. Before operaor s upgrade e.g., T in Fig., he number of oal users in each nework does no change; 5 afer operaor s upgrade, operaor s and he oher operaors users swich o he new service a raes λ and αλ, respecively. By considering 3, 4, and he decreasing cos Ke UT, operaor s long-erm profi when choosing an upgrade ime T is π T = π, T + π,>t Ke UT = e ST S + γ + γ λ + S αλ + S e ST γ λ + S + γ Ke UT αλ + S K mono h = γ + e ST γ + αλ + S + γ S. 5 e ST We can show ha π T in 5 is sricly concave in T, hus we can compue he opimal upgrade ime T by solving he firs-order condiion. The opimal upgrade ime depends on he following upgrade cos hreshold in he monopoly marke, λ+s + αλ+s λ+s + +αλ+s U/S S αλ+s + γ γ. 6 U Theorem : Operaor s opimal upgrade ime in a monopoly marke is: Low cos regime upgrade cos K Kh mono : operaor upgrades a T =. High cos regime K > Kh mono : operaor upgrades a T = K U S log Kh mono >. 7 Inuiively, an early upgrade gives operaor a larger marke share and enables him o ge a higher revenue via he more efficien service. Such advanage is especially obvious in he low cos regime where he upgrade cos K is small. ex we focus on he high cos regime, and explore how he nework parameers affec operaor s upgrade ime. Observaion : Operaor s opimal upgrade ime T increases wih he upgrade cos K, and decreases wih α i.e., increases wih he users iner-nework swiching cos. The proofs of Observaion and he following observaions are given in our online echnical repor []. Observaion Figure : When h < K < U S Kmono h, T firs increases and hen decreases in U. When K U S Kmono h, T monoonically decreases in U. Figure shows T as a funcion of U and K. When K is large or U is large, operaor wans o pospone his upgrade unil he upgrade cos decreases significanly. A larger U hus K mono 5 I is possible for users o swich beween neworks in he same service class, bu such minor swiching does no change he average marke shares.

5 Opimal upgrade decision T K=.4 K=.8 K= Discouning rae of upgrade cos U Fig.. Operaor s opimal upgrade ime T as a funcion of cos K and he discoun rae U of cos. Oher parameers are =, = 5, S =, λ =, and α =.5. Opimal upgrade ime T /=3% /=5% /=7% Efficiency raio beween and services γ Fig. 3. Operaor s opimal upgrade ime T as a funcion of he efficiency raio beween and services γ and his original marke share. Oher parameers are =, K =, S =, λ =, and U =. a faser cos-decreasing rae srenghens his willingness o pospone. When K is small and U is small, he upgrade cos is small and does no decrease fas enough. In his case, operaor chooses o upgrade early if he revenue increase can compensae for he small upgrade cos. Observaion 3 Figure 3: When operaor s original marke share is large, T increases in he efficiency raio γ beween and. When is small, T decreases in γ. Figure 3 shows T as a funcion of γ and. When is large, operaor canno arac many users from oher operaors and has smaller incenives o upgrade. As γ increases and hus he QoS gap beween and shrinks, he is less ineresed in service and hus pospones his upgrade. When is small, operaor has limied marke share and can arac many more users by upgrading early. As γ increases, operaor obains a higher revenue beween his exising users and he increasing number of users. Operaor, however, does no benefi much from his, as he loses his marke share due o operaor s services. Thus T decreases in γ. V. COMPETITIO MARKET: DUOPOLY MODEL AD GAME FORMULATIO In his secion, we focus on he compeiion beween muliple operaors who can choose o upgrade o services. To make he analysis racable and o derive clear engineering insighs, we focus on he case of wo operaors duopoly in his paper. This analysis serves as he firs sep in undersanding he more general oligopoly case. This duopoly model is reasonable in a counry like China, where China Mobile and China Unicom are he wo dominan cellular operaors in he marke. A similar siuaion exiss in several oher Asian and European counries as well. The focus of his and he following secion is o undersand why in so many exising indusry examples e.g., [3] [5] operaors choose o upgrade o services a differen imes even hough hey have he resources o upgrade simulaneously. In paricular, we examine wheher such asymmeric upgrades emerge even when he wo operaors are similar e.g., having similar marke shares before upgrades e.g., Verizon has 6.3 million users and AT&T has 98.6 million users in he US. In our online echnical repor [], we also examine he case where neworks are heerogeneous in naure, and we show ha asymmeric operaors e.g., wih differen marke shares have more incenives o upgrade a differen imes. Thus in he following analysis we can consider wo operaors ha have he same marke shares before he upgrades =, he same upgrade cos K, and he same cos discoun rae U. We will firs derive he operaors profis under any upgrade decisions, and hen analyze he duopoly game where each operaor chooses he bes upgrade ime o maximize his profi. A. Operaors Long-erm Profis Le us denoe wo operaors upgrade imes as T and T, respecively. Because he wo operaors are symmeric, wihou loss of generaliy, we assume in he following example before Lemma ha operaor upgrades no laer han operaor i.e., T T. To calculae he operaors profis, we firs need o undersand how users churn from o services, and how his affecs he operaors revenue raes over ime. Figure 4 shows ha user churn is differen in hree phases, depending on how many operaors have upgraded. Phase I T : o operaor has upgraded and boh operaors marke shares do no change. Phase II T < T : Operaor has upgraded o service bu operaor has no. The users of wo operaors swich o operaor s service a differen raes. The numbers of users in he operaors differen services are = e λ T, = e αλ T, and = e λ T e αλ T. Phase III > T : Boh operaors have upgraded, and users only swich o he service of heir curren operaor. The numbers of users in operaors differen services are = e λ T, = e λ T e αλt T, = eαλt T λ T,

6 - - - T T Phase I T T Phase II T T Phase III Fig. 4. Users swiches over he operaors services: Phase I wih services only, Phase II wih operaor s service, and Phase III wih boh operaors services. Operaor s users: Operaor s users: T Operaor s users: Operaor s users: T Fig. 5. The numbers of users in he operaors differen services as funcions of ime. Here, operaor chooses his upgrade ime a T and operaor chooses T wih T T. and = eαλt T e λ T. Figure 5 summarizes how users churn in he hree phases. Similar o Secion IV, we can derive operaors revenue raes based on users churn over ime. By inegraing each operaor s revenue rae over all hree phases, we obain ha operaor s long-erm revenue. Recall ha an operaor s profi is he difference beween his revenue and he one-ime upgrade cos. By furher considering he symmeric case of T T, we have he following resul. Lemma : Consider wo operaors i, j {, } wih i j upgrading a T i and T { j. Operaor i s long-erm profi is π ER T i, T j, if T i T j ; π i T i, T j = π LT 8 T j, T i, if T i T j, where π ER T i, T j and π LT T j, T i are given in 9 and, respecively. oe ha an operaor s profi π i T i, T j is coninuous in his upgrade ime T i. When operaor i s upgrade ime T i is less han T j, he increases his marke share a rae αλ during he ime period from T i o T j ; bu when T i > T j, operaor i loses his marke share a rae αλ during he period from T j o T i. This explains why we need wo differen funcions π ER T i, T j and π LT T j, T i o compleely characerize he long-erm profi for each operaor. B. Duopoly Upgrade Game ex we consider he non-cooperaive game heoreical ineracions beween wo operaors, where each of hem seeks o maximize his long-erm profi by choosing he bes upgrade ime. Upgrade Game: We model he compeiion beween wo operaors as follows: Players: Operaors and. Sraegy spaces: Operaor i {, } can choose upgrade ime T i from he feasible se T i = [, ]. 6 Payoff funcions: Operaor i {, } wans o maximize his profi π i T i, T j defined in 8. oice ha we consider a saic game here, where boh operaors decide when o upgrade a he beginning of ime. This is moivaed by he fac ha operaors usually make long-erm decisions in pracice raher han changing decisions frequenly, as many upgrade operaions e.g., financial budge and echnological rials need o be planned and prepared. As we consider ha each operaor has complee informaion abou his compeior s and users parameers, he will no deviae from his iniial decision as ime goes on. Also, i should be poined ou ha in many compeiion markes operaors can obain available resource for upgrade a a similar ime as we menioned a he beginning of his secion. Afer making decision a =, one operaor does no change his decision laer on. This is reasonable when operaors can predic he fuure marke adopion. 7 In Secion VI, we analyze he duopoly upgrade game under differen swiching coss i.e., he value of α,. ash equilibrium is a commonly used soluion concep for a saic game. A a ash equilibrium, no player can increase his payoff by deviaing unilaerally [9]. We are ineresed in characerizing he condiions under which an asymmeric upgrade equilibrium emerges beween symmeric operaors. VI. COMPETITIO MARKET: PRACTICAL ITER-ETWORK SWITCHIG RATE In his secion, we consider he case of α >, i.e., users may swich o he service of a differen operaor. The equilibrium analysis in his general case depends on he relaionship beween U upgrade cos discoun rae and S money depreciaion rae. We assume ha U is much larger han S, i.e., U > S + αλ. This represens he pracical case where he advance of echnology is he dominan facor in deermining U, and no many users choose o swich operaors when he service is jus deployed i.e., small α [7]. For example, Sprin deployed he firs nework in US by using WiMAX echnology in 8 when LTE echnology 6 oe ha T i = means ha operaor i never upgrades. 7 Operaors can predic he fuure marke adopion by exploring hisorical records of he marke and some rial of deploymen. In he fuure we will sudy he incomplee informaion case, where an operaor may learn more informaion as he ime goes and revise his upgrade decision if he has no upgraded ye.

7 π ER T i, T j = γ + γe ST i e αλt j T i ST j S + γ e ST i + e +αλt j T i ST j λ + S γ λ + S e αλt j T i ST j π LT T j, T i = e αλt i T j ST i + γe ST i e αλt j T i ST j αλ + S + e ST i e +αλt j T i ST j + αλ + S e λt j T i + e αλt j T i γ e ST i λ + S S γ λ + S γ e λt i T j + e αλt i T j λ + S λ + S + e ST i e αλt j T i ST j αλ + S Ke UT i. 9 + γ S e ST j γ αλ + S e ST j e αλt i T j ST i Ke UT i. was no maure ye. Only wo years laer, in, LTE could already offer a much lower cos per bi han WiMAX [3]. From, LTE is expeced o be he leading echnology choice for neworks. This example moivaes ha U is much larger han S, and we will sudy wheher he operaors symmeric upgrades happen in his scenario. Recall ha by upgrading a T and T, he operaors receive he profis given in 8. In game heory, one operaor s bes response funcion is his upgrade ime ha achieves he larges long-erm profi, as a funcion of a fixed upgrade ime of he oher operaor [9]. A fixed poin of he wo operaors bes response funcions is he ash equilibrium, and in general here can be more han one such fixed poin. We can show ha he operaors bes responses funcions T bes T and T bes T depend on he upgrade cos K, and in paricular, hey depend on wo cos hresholds K comp h < K comp h ha lead o hree cos regimes: low, medium, and high. When he upgrade cos K is less han he firs hreshold i.e., low cos regime, boh operaors will upgrade a = o maximize he revenue from he service. By solving π LT, T i Ti= =, i {, }, T i K comp h we have K comp h = αλ γ λ + S + αλ S γ λ + 3αλ + S λ + S λ + S U. When he upgrade cos K is larger han K comp h i.e., medium or high cos regimes, a leas one operaor pospones his upgrade unil he upgrade cos decreases sufficienly. In paricular, when K is larger han he second hreshold K comp h i.e., high cos regime, boh operaors pospone heir upgrades. When operaor i {, } upgrades a =, operaor j i pospones his upgrade o Tj bes, which is he unique soluion o π LT, T j T Tj=Tj bes =. j The hreshold K comp h can be obained by solving π ER T i, Tj bes Ti= =. 3 T i Operaor s upgrade ime T K=.6: E K=.58: E K=.58: E K=.6: E K=.58: T bes T K=.58: T bes T K=.6: T bes T K=.6: T bes T Operaor s upgrade ime T Fig. 6. Two operaors bes upgrade responses o each oher according o differen cos values in he medium cos regime. Oher parameers are α =.5, =, U =, S =, λ = and γ =.5 such ha U > S + αλ. ex we illusrae numerically how he wo operaors bes response funcions T bes T and T bes T change wih he upgrade cos K. Figure 6 shows ha each operaor s bes response funcion is disconinuous in he medium cos regime, and he wo bes response funcions wih he same value of K inersec a wo poins: = T < T and symmerically = T < T. To illusrae his siuaion, consider operaor s bes response T bes T in he case K =.6. If operaor upgrades early such ha T is less han.5, operaor does no upgrade a he same ime o avoid a severe compeiion. If operaor upgrades laer such ha T is larger han.5, operaor chooses o upgrade earlier han operaor o increase his marke share. Thus T bes T is disconinuous a T =.5. Figure 7 shows ha each operaor s bes response funcion is disconinuous in he high cos regime, and he wo funcions wih he same value of K inersec a wo poins, equilibria < T < T and symmerically < T < T. Unlike Fig. 6, he high cos here prevens any operaor from choosing he upgrade ime =. Figure 8 summarizes how operaors upgrade equilibrium changes as cos K increases: saring wih Ti = Tj = in low cos regime, hen = Ti < Tj wih increasing T j in medium cos regime, and finally < Ti < Tj wih increasing T and T in high cos regime. In he following heorem, we prove ha he operaors do no choose symmeric upgrades as long as he cos is no low. Theorem : The wo operaors upgrade equilibria sa-

8 Operaor s upgrade ime T K=.7: E. K=.7: E K=.87: E K=.87: E K=.7:T bes T K=.7:T bes T K=.87:T bes T K=.87:T bes T Operaor s upgrade ime T Operaor s equilibrium profi π E : T T E : T T Medium cos regime: π <π as K High cos regime: π <π as K Low cos regime: π =π as K Operaor s equilibrium profi π Fig. 7. Two operaors bes upgrade responses o each oher according o differen cos values in he high cos regime. Oher parameers are α =.5, =, U =, S =, λ = and γ =.5 such ha U > S + αλ. Fig. 9. Two operaors equilibrium profis π,π change as cos K increases under large γ =.5. Oher parameers are α =.5, =, U =, S =, and λ = such ha U > S + αλ. Operaor s equilibrium ime T High cos regime: <T <T : as K Medium cos regime: =T <T as K E : T T E : T T Low cos regime: =T =T as K Operaor s equilibrium ime T Fig. 8. Two operaors equilibrium T,T changes as cos K increases. Oher parameers are α =.5, =, U =, S =, λ =, and γ =.5 such ha U > S + αλ. isfy he following properies: Low cos regime K K comp h : Boh operaors upgrade a T = T =. Medium cos regime K comp h < K K comp h : Operaors do no upgrade a he same ime, and only one operaor may upgrade a =. The possible equilibria can only be T < T and symmerically T < T. High cos regime K > K comp h : Operaors do no upgrade a he same ime, and none of hem upgrade a =. The possible equilibria can only be < T < T and symmerically < T < T. The proof of Theorem is given in our online repor []. To undersand he inuiion behind he asymmeric srucure, we summarize he advanages of earlier and laer upgrades wih α > as follows: Earlier upgrade gives an operaor he advanage o arac more users from he oher operaor, and enables he operaor o collec a higher revenue from he service. Laer upgrade allows an operaor o incur a reduced upgrade cos and o ake advanage of he nework effec in he marke wih more exising users when he upgrades. In order o fully enjoy he wo advanages of earlier or laer upgrades, operaors will avoid symmeric upgrade. If one operaor upgrades much earlier o capure a larger marke share ha can compensae for a large upgrade cos, he second operaor will no upgrade a he same ime o avoid severe compeiion in marke share; insead, he second operaor will wai unil his loss of users and revenue is compensaed by he reducion of upgrade cos wih U > S + αλ. ex we sudy how operaors equilibrium profis change wih cos K and he economic efficiency raio γ beween and services in he hree cos regimes. oe ha an operaor may or may no be able o charge a significanly higher price from a user hough does improve a lo over in QoS. Figures 9 and show operaors equilibrium profis under large and small γ values, respecively. We firs sudy he large γ scenario in Fig. 9 which means an operaor o charge a slighly higher price in service han. Wihou loss of generaliy, we focus on he case where operaor upgrades no laer han operaor i.e., T T. In he low cos regime, by upgrading a T = T =, he wo operaors profis are he same and decrease wih cos K. In he medium cos regime, Fig. 9 shows ha operaor receives a larger profi han operaor by upgrading a T =. Perhaps surprisingly, his profi increases wih K, whereas operaor s profi decreases wih K. Inuiively, he increase of K encourages operaor o furher pospone his upgrade and lose more users o operaor. The change of operaor s profi rades off he increases of his marke share and upgrade cos. As operaor s marke share increases, his growing users communicae more wih his users via he efficien service under large γ. Operaor s revenue increases because of a more efficien inra-nework raffic, which helps compensae for he upgrade cos. In he high cos regime, Fig. 9 shows ha boh operaors have o pospone heir upgrades and, surprisingly, boh operaors profis increase wih K. As K increases, operaor furher pospones his upgrade and operaor

9 Operaor s equilibrium profi π E : T T E : T T High cos regime: π <π as K Low cos regime: π =π as K Medium cos regime: π <π as K Operaor s equilibrium profi π selec asymmeric upgrade imes o avoid severe compeiion. Compared o duopoly, he operaor who is he las o upgrade loses more marke share o he ohers and bu enjoys he smalles upgrade cos and he larges nework effec. I is also ineresing o sudy operaors usage of plan announcemens before acual upgrades. One operaor who acually decides o upgrades laer han wha he announces can preven some of his users swiching o oher neworks. We can use a signaling game o sudy operaors announcemens. Moreover, we can sudy operaors mixed sraegies in upgrades, where one operaor chooses a probabiliy disribuion of upgrading a differen imes. Alhough heoreically ineresing, mixed sraegies are hard o implemen in pracice [9]. Fig.. Two operaors equilibrium profis π,π change as cos K increases under small γ =.. Oher parameers are α =.5, =, U =, S =, and λ = such ha U > S + αλ. s marke share decreases more slowly. Thus operaors compeiion in he marke share is posponed, and under large γ operaor can obain more revenue before operaor s upgrade. Operaor, on he oher hand, also benefis from his posponemen o decrease his upgrade cos. Since operaor also pospones his upgrade, operaor can sill capure a large marke share even hough he upgrades laer. As K, no operaor upgrades and operaors profis approach he symmeric profis. Under large γ, he service is no much beer han and he availabiliy of upgrade only inensifies operaors compeiion. Compared o radiional scenario, boh operaors profis decrease when he upgrade cos is high. In oher words, boh operaors will be beer off if echnology is no available in his case. Figure shows how operaors profis change wih K under small γ. The resuls are more inuiive; his is because he operaors profis decrease wih K in all hree cos regimes. Under small γ, he availabiliy of he upgrade significanly improves he revenue in each nework. A larger K reduces he benefi of upgrades. However, he operaors profis will no be smaller afer he upgrade under any value of K. VII. COCLUSIOS AD FUTURE WORK This paper presens he firs analyical sudy of operaors upgrade decisions. We firs analyze a monopoly marke, where he monopolis s opimal upgrade ime rades off an increased marke share and he decreasing upgrade cos. We hen develop a non-cooperaive game model o sudy he compeiion beween operaors. Our resuls show ha operaors selec differen upgrade imes o avoid severe compeiion in marke share. We furher show ha he availabiliy of upgrade may decrease boh operaors profis due o heir compeiion, and heir profis may increase wih he upgrade cos. There are some possible ways o exend he resuls in his paper. For example, we could consider an oligopoly marke wih more han wo compeiive operaors. Inuiively, muliple operaors under iner-nework swiching would sill REFERECES [] S. Hui and K. Yeung, Challenges in he migraion o mobile sysems, IEEE Commun. Magazine, vol. 4, pp , 3. [] ITU Press Release, ITU world radiocommunicaion seminar highlighs fuure communicaion echnologies, Dec.. [Online]. Available: hp:// releases//48.aspx [3] Acionec Corporaion, LTE marke upgrade, Whie Paper,. [4] Xinhua, China Mobile ambiious o lead ech, China Daily,. [5] E. Saviz, Verizon, AT&T Big Winners In 7 MHz Aucion, The Wall Sree Journal- Digial ework, Mar. 8. [6] M. Reardon, Sprin exel and Clearwire deail plans, CET ews, May 8. [7] B. Briscoe, A. Odlyzko, and B. Tilly, Mecalfe s law is wrongcommunicaions neworks increase in value as hey add members-bu by how much? IEEE Specrum, vol. 43, no. 7, pp , 6. [8] J. Musacchio, J. Walrand, and S. Wu, A game heoreic model for nework upgrade decisions, Alleron Conference, 6. [9] L. Jiang, V. Ananharam, and J. Walrand, How bad are selfish invesmens in nework securiy? IEEE/ACM Transacions on eworking, vol. 9, no., pp ,. [] S. Sen, Y. Jin, R. Guerin, and K. Hosanagar, Modeling he dynamics of nework echnology adopion and he role of converers, IEEE/ACM Transacions on eworking, vol. 8, no. 6, pp ,. [] EUROPA, Terminaion raes: Quesions and Answers, MEMO/8/438, Brussels, Jun. 8. [] P. Klemperer, Compeiion when consumers have swiching coss: An overview wih applicaions o indusrial organizaion, macroeconomics, and inernaional rade, The Review of Economic Sudies, vol. 6, no. 4, pp , 995. [3] R. Beck. The neworked economy: he naure, adopion and diffusion of communicaion sandards, Wiesbaden, 6. [4] R. Dewener and J. Haucap, The effecs of regulaing mobile erminaion raes for asymmeric neworks, European Journal of Law and Economics, vol., no., pp , 5. [5] C. Harrison, Mexico s Big Cellular Problem: Carlos Slim, Bloomberg Businessweek, May. [6] A. Chiang. Fundamenal mehods of mahemaical economics. McGraw- Hill Book Co., ew York, 967. [7] E. Saviz, Sprin is sruggling o ge subscribers, analys says, The Wall Sree Journal-Digial eworks,. [8] J. Dohery. Verizon communicaions managemen discusses q resuls- earnings call ranscrip. Apr.. [9] D. Fudenberg and J. Tirole, Game Theory, MIT Press, 99. [] L. Duan, J. Huang, and J. Walrand, Economic analysis of nework upgrade, Tech. Rep. [Online]. Available: hp://jianwei.ie.cuhk.edu.hk/ publicaion/techreporupgrade.pdf

Chapter 1.6 Financial Management

Chapter 1.6 Financial Management Chaper 1.6 Financial Managemen Par I: Objecive ype quesions and answers 1. Simple pay back period is equal o: a) Raio of Firs cos/ne yearly savings b) Raio of Annual gross cash flow/capial cos n c) = (1

More information

PROFIT TEST MODELLING IN LIFE ASSURANCE USING SPREADSHEETS PART ONE

PROFIT TEST MODELLING IN LIFE ASSURANCE USING SPREADSHEETS PART ONE Profi Tes Modelling in Life Assurance Using Spreadshees PROFIT TEST MODELLING IN LIFE ASSURANCE USING SPREADSHEETS PART ONE Erik Alm Peer Millingon 2004 Profi Tes Modelling in Life Assurance Using Spreadshees

More information

Market Liquidity and the Impacts of the Computerized Trading System: Evidence from the Stock Exchange of Thailand

Market Liquidity and the Impacts of the Computerized Trading System: Evidence from the Stock Exchange of Thailand 36 Invesmen Managemen and Financial Innovaions, 4/4 Marke Liquidiy and he Impacs of he Compuerized Trading Sysem: Evidence from he Sock Exchange of Thailand Sorasar Sukcharoensin 1, Pariyada Srisopisawa,

More information

Chapter 8: Regression with Lagged Explanatory Variables

Chapter 8: Regression with Lagged Explanatory Variables Chaper 8: Regression wih Lagged Explanaory Variables Time series daa: Y for =1,..,T End goal: Regression model relaing a dependen variable o explanaory variables. Wih ime series new issues arise: 1. One

More information

Performance Center Overview. Performance Center Overview 1

Performance Center Overview. Performance Center Overview 1 Performance Cener Overview Performance Cener Overview 1 ODJFS Performance Cener ce Cener New Performance Cener Model Performance Cener Projec Meeings Performance Cener Execuive Meeings Performance Cener

More information

Analysis of Pricing and Efficiency Control Strategy between Internet Retailer and Conventional Retailer

Analysis of Pricing and Efficiency Control Strategy between Internet Retailer and Conventional Retailer Recen Advances in Business Managemen and Markeing Analysis of Pricing and Efficiency Conrol Sraegy beween Inerne Reailer and Convenional Reailer HYUG RAE CHO 1, SUG MOO BAE and JOG HU PARK 3 Deparmen of

More information

Individual Health Insurance April 30, 2008 Pages 167-170

Individual Health Insurance April 30, 2008 Pages 167-170 Individual Healh Insurance April 30, 2008 Pages 167-170 We have received feedback ha his secion of he e is confusing because some of he defined noaion is inconsisen wih comparable life insurance reserve

More information

The Grantor Retained Annuity Trust (GRAT)

The Grantor Retained Annuity Trust (GRAT) WEALTH ADVISORY Esae Planning Sraegies for closely-held, family businesses The Granor Reained Annuiy Trus (GRAT) An efficien wealh ransfer sraegy, paricularly in a low ineres rae environmen Family business

More information

LEASING VERSUSBUYING

LEASING VERSUSBUYING LEASNG VERSUSBUYNG Conribued by James D. Blum and LeRoy D. Brooks Assisan Professors of Business Adminisraion Deparmen of Business Adminisraion Universiy of Delaware Newark, Delaware The auhors discuss

More information

Single-machine Scheduling with Periodic Maintenance and both Preemptive and. Non-preemptive jobs in Remanufacturing System 1

Single-machine Scheduling with Periodic Maintenance and both Preemptive and. Non-preemptive jobs in Remanufacturing System 1 Absrac number: 05-0407 Single-machine Scheduling wih Periodic Mainenance and boh Preempive and Non-preempive jobs in Remanufacuring Sysem Liu Biyu hen Weida (School of Economics and Managemen Souheas Universiy

More information

Why Did the Demand for Cash Decrease Recently in Korea?

Why Did the Demand for Cash Decrease Recently in Korea? Why Did he Demand for Cash Decrease Recenly in Korea? Byoung Hark Yoo Bank of Korea 26. 5 Absrac We explores why cash demand have decreased recenly in Korea. The raio of cash o consumpion fell o 4.7% in

More information

Niche Market or Mass Market?

Niche Market or Mass Market? Niche Marke or Mass Marke? Maxim Ivanov y McMaser Universiy July 2009 Absrac The de niion of a niche or a mass marke is based on he ranking of wo variables: he monopoly price and he produc mean value.

More information

USE OF EDUCATION TECHNOLOGY IN ENGLISH CLASSES

USE OF EDUCATION TECHNOLOGY IN ENGLISH CLASSES USE OF EDUCATION TECHNOLOGY IN ENGLISH CLASSES Mehme Nuri GÖMLEKSİZ Absrac Using educaion echnology in classes helps eachers realize a beer and more effecive learning. In his sudy 150 English eachers were

More information

Morningstar Investor Return

Morningstar Investor Return Morningsar Invesor Reurn Morningsar Mehodology Paper Augus 31, 2010 2010 Morningsar, Inc. All righs reserved. The informaion in his documen is he propery of Morningsar, Inc. Reproducion or ranscripion

More information

Multiprocessor Systems-on-Chips

Multiprocessor Systems-on-Chips Par of: Muliprocessor Sysems-on-Chips Edied by: Ahmed Amine Jerraya and Wayne Wolf Morgan Kaufmann Publishers, 2005 2 Modeling Shared Resources Conex swiching implies overhead. On a processing elemen,

More information

ARCH 2013.1 Proceedings

ARCH 2013.1 Proceedings Aricle from: ARCH 213.1 Proceedings Augus 1-4, 212 Ghislain Leveille, Emmanuel Hamel A renewal model for medical malpracice Ghislain Léveillé École d acuaria Universié Laval, Québec, Canada 47h ARC Conference

More information

SKF Documented Solutions

SKF Documented Solutions SKF Documened Soluions Real world savings and we can prove i! How much can SKF save you? Le s do he numbers. The SKF Documened Soluions Program SKF is probably no he firs of your supplier parners o alk

More information

DYNAMIC MODELS FOR VALUATION OF WRONGFUL DEATH PAYMENTS

DYNAMIC MODELS FOR VALUATION OF WRONGFUL DEATH PAYMENTS DYNAMIC MODELS FOR VALUATION OF WRONGFUL DEATH PAYMENTS Hong Mao, Shanghai Second Polyechnic Universiy Krzyszof M. Osaszewski, Illinois Sae Universiy Youyu Zhang, Fudan Universiy ABSTRACT Liigaion, exper

More information

Measuring macroeconomic volatility Applications to export revenue data, 1970-2005

Measuring macroeconomic volatility Applications to export revenue data, 1970-2005 FONDATION POUR LES ETUDES ET RERS LE DEVELOPPEMENT INTERNATIONAL Measuring macroeconomic volailiy Applicaions o expor revenue daa, 1970-005 by Joël Cariolle Policy brief no. 47 March 01 The FERDI is a

More information

Automatic measurement and detection of GSM interferences

Automatic measurement and detection of GSM interferences Auomaic measuremen and deecion of GSM inerferences Poor speech qualiy and dropped calls in GSM neworks may be caused by inerferences as a resul of high raffic load. The radio nework analyzers from Rohde

More information

Mathematics in Pharmacokinetics What and Why (A second attempt to make it clearer)

Mathematics in Pharmacokinetics What and Why (A second attempt to make it clearer) Mahemaics in Pharmacokineics Wha and Why (A second aemp o make i clearer) We have used equaions for concenraion () as a funcion of ime (). We will coninue o use hese equaions since he plasma concenraions

More information

Duration and Convexity ( ) 20 = Bond B has a maturity of 5 years and also has a required rate of return of 10%. Its price is $613.

Duration and Convexity ( ) 20 = Bond B has a maturity of 5 years and also has a required rate of return of 10%. Its price is $613. Graduae School of Business Adminisraion Universiy of Virginia UVA-F-38 Duraion and Convexiy he price of a bond is a funcion of he promised paymens and he marke required rae of reurn. Since he promised

More information

We consider a decentralized assembly system in which a buyer purchases components from several first-tier

We consider a decentralized assembly system in which a buyer purchases components from several first-tier MANAGEMENT SCIENCE Vol. 55, No. 4, April 2009, pp. 552 567 issn 0025-1909 eissn 1526-5501 09 5504 0552 informs doi 10.1287/mnsc.1080.0961 2009 INFORMS Dynamic Cos Reducion Through Process Improvemen in

More information

CRISES AND THE FLEXIBLE PRICE MONETARY MODEL. Sarantis Kalyvitis

CRISES AND THE FLEXIBLE PRICE MONETARY MODEL. Sarantis Kalyvitis CRISES AND THE FLEXIBLE PRICE MONETARY MODEL Saranis Kalyviis Currency Crises In fixed exchange rae regimes, counries rarely abandon he regime volunarily. In mos cases, raders (or speculaors) exchange

More information

BALANCE OF PAYMENTS. First quarter 2008. Balance of payments

BALANCE OF PAYMENTS. First quarter 2008. Balance of payments BALANCE OF PAYMENTS DATE: 2008-05-30 PUBLISHER: Balance of Paymens and Financial Markes (BFM) Lena Finn + 46 8 506 944 09, lena.finn@scb.se Camilla Bergeling +46 8 506 942 06, camilla.bergeling@scb.se

More information

The Application of Multi Shifts and Break Windows in Employees Scheduling

The Application of Multi Shifts and Break Windows in Employees Scheduling The Applicaion of Muli Shifs and Brea Windows in Employees Scheduling Evy Herowai Indusrial Engineering Deparmen, Universiy of Surabaya, Indonesia Absrac. One mehod for increasing company s performance

More information

Table of contents Chapter 1 Interest rates and factors Chapter 2 Level annuities Chapter 3 Varying annuities

Table of contents Chapter 1 Interest rates and factors Chapter 2 Level annuities Chapter 3 Varying annuities Table of conens Chaper 1 Ineres raes and facors 1 1.1 Ineres 2 1.2 Simple ineres 4 1.3 Compound ineres 6 1.4 Accumulaed value 10 1.5 Presen value 11 1.6 Rae of discoun 13 1.7 Consan force of ineres 17

More information

Making a Faster Cryptanalytic Time-Memory Trade-Off

Making a Faster Cryptanalytic Time-Memory Trade-Off Making a Faser Crypanalyic Time-Memory Trade-Off Philippe Oechslin Laboraoire de Securié e de Crypographie (LASEC) Ecole Polyechnique Fédérale de Lausanne Faculé I&C, 1015 Lausanne, Swizerland philippe.oechslin@epfl.ch

More information

Option Put-Call Parity Relations When the Underlying Security Pays Dividends

Option Put-Call Parity Relations When the Underlying Security Pays Dividends Inernaional Journal of Business and conomics, 26, Vol. 5, No. 3, 225-23 Opion Pu-all Pariy Relaions When he Underlying Securiy Pays Dividends Weiyu Guo Deparmen of Finance, Universiy of Nebraska Omaha,

More information

THE FIRM'S INVESTMENT DECISION UNDER CERTAINTY: CAPITAL BUDGETING AND RANKING OF NEW INVESTMENT PROJECTS

THE FIRM'S INVESTMENT DECISION UNDER CERTAINTY: CAPITAL BUDGETING AND RANKING OF NEW INVESTMENT PROJECTS VII. THE FIRM'S INVESTMENT DECISION UNDER CERTAINTY: CAPITAL BUDGETING AND RANKING OF NEW INVESTMENT PROJECTS The mos imporan decisions for a firm's managemen are is invesmen decisions. While i is surely

More information

Chapter 7. Response of First-Order RL and RC Circuits

Chapter 7. Response of First-Order RL and RC Circuits Chaper 7. esponse of Firs-Order L and C Circuis 7.1. The Naural esponse of an L Circui 7.2. The Naural esponse of an C Circui 7.3. The ep esponse of L and C Circuis 7.4. A General oluion for ep and Naural

More information

Chapter 6: Business Valuation (Income Approach)

Chapter 6: Business Valuation (Income Approach) Chaper 6: Business Valuaion (Income Approach) Cash flow deerminaion is one of he mos criical elemens o a business valuaion. Everyhing may be secondary. If cash flow is high, hen he value is high; if he

More information

4. International Parity Conditions

4. International Parity Conditions 4. Inernaional ariy ondiions 4.1 urchasing ower ariy he urchasing ower ariy ( heory is one of he early heories of exchange rae deerminaion. his heory is based on he concep ha he demand for a counry's currency

More information

Advise on the development of a Learning Technologies Strategy at the Leopold-Franzens-Universität Innsbruck

Advise on the development of a Learning Technologies Strategy at the Leopold-Franzens-Universität Innsbruck Advise on he developmen of a Learning Technologies Sraegy a he Leopold-Franzens-Universiä Innsbruck Prof. Dr. Rob Koper Open Universiy of he Neherlands Educaional Technology Experise Cener Conex - Period

More information

Optimal Investment and Consumption Decision of Family with Life Insurance

Optimal Investment and Consumption Decision of Family with Life Insurance Opimal Invesmen and Consumpion Decision of Family wih Life Insurance Minsuk Kwak 1 2 Yong Hyun Shin 3 U Jin Choi 4 6h World Congress of he Bachelier Finance Sociey Torono, Canada June 25, 2010 1 Speaker

More information

Research on Inventory Sharing and Pricing Strategy of Multichannel Retailer with Channel Preference in Internet Environment

Research on Inventory Sharing and Pricing Strategy of Multichannel Retailer with Channel Preference in Internet Environment Vol. 7, No. 6 (04), pp. 365-374 hp://dx.doi.org/0.457/ijhi.04.7.6.3 Research on Invenory Sharing and Pricing Sraegy of Mulichannel Reailer wih Channel Preference in Inerne Environmen Hanzong Li College

More information

CHARGE AND DISCHARGE OF A CAPACITOR

CHARGE AND DISCHARGE OF A CAPACITOR REFERENCES RC Circuis: Elecrical Insrumens: Mos Inroducory Physics exs (e.g. A. Halliday and Resnick, Physics ; M. Sernheim and J. Kane, General Physics.) This Laboraory Manual: Commonly Used Insrumens:

More information

Double Entry System of Accounting

Double Entry System of Accounting CHAPTER 2 Double Enry Sysem of Accouning Sysem of Accouning \ The following are he main sysem of accouning for recording he business ransacions: (a) Cash Sysem of Accouning. (b) Mercanile or Accrual Sysem

More information

Mobile Broadband Rollout Business Case: Risk Analyses of the Forecast Uncertainties

Mobile Broadband Rollout Business Case: Risk Analyses of the Forecast Uncertainties ISF 2009, Hong Kong, 2-24 June 2009 Mobile Broadband Rollou Business Case: Risk Analyses of he Forecas Uncerainies Nils Krisian Elnegaard, Telenor R&I Agenda Moivaion Modelling long erm forecass for MBB

More information

To Sponsor or Not to Sponsor: Sponsored Search Auctions with Organic Links and Firm Dependent Click-Through Rates

To Sponsor or Not to Sponsor: Sponsored Search Auctions with Organic Links and Firm Dependent Click-Through Rates To Sponsor or No o Sponsor: Sponsored Search Aucions wih Organic Links and Firm Dependen Click-Through Raes Michael Arnold, Eric Darmon and Thierry Penard June 5, 00 Draf: Preliminary and Incomplee Absrac

More information

Journal Of Business & Economics Research September 2005 Volume 3, Number 9

Journal Of Business & Economics Research September 2005 Volume 3, Number 9 Opion Pricing And Mone Carlo Simulaions George M. Jabbour, (Email: jabbour@gwu.edu), George Washingon Universiy Yi-Kang Liu, (yikang@gwu.edu), George Washingon Universiy ABSTRACT The advanage of Mone Carlo

More information

Trading on Short-Term Information

Trading on Short-Term Information 428 Trading on Shor-Term Informaion by ALEXANDER GÜMBEL This paper shows ha invesors may wan fund managers o acquire and rade on shor-erm insead of more profiable long-erm informaion. This improves learning

More information

Price elasticity of demand for crude oil: estimates for 23 countries

Price elasticity of demand for crude oil: estimates for 23 countries Price elasiciy of demand for crude oil: esimaes for 23 counries John C.B. Cooper Absrac This paper uses a muliple regression model derived from an adapaion of Nerlove s parial adjusmen model o esimae boh

More information

TEMPORAL PATTERN IDENTIFICATION OF TIME SERIES DATA USING PATTERN WAVELETS AND GENETIC ALGORITHMS

TEMPORAL PATTERN IDENTIFICATION OF TIME SERIES DATA USING PATTERN WAVELETS AND GENETIC ALGORITHMS TEMPORAL PATTERN IDENTIFICATION OF TIME SERIES DATA USING PATTERN WAVELETS AND GENETIC ALGORITHMS RICHARD J. POVINELLI AND XIN FENG Deparmen of Elecrical and Compuer Engineering Marquee Universiy, P.O.

More information

NASDAQ-100 Futures Index SM Methodology

NASDAQ-100 Futures Index SM Methodology NASDAQ-100 Fuures Index SM Mehodology Index Descripion The NASDAQ-100 Fuures Index (The Fuures Index ) is designed o rack he performance of a hypoheical porfolio holding he CME NASDAQ-100 E-mini Index

More information

The Complete VoIP Telecom Service Provider The Evolution of a SIP Trunking Provider

The Complete VoIP Telecom Service Provider The Evolution of a SIP Trunking Provider The Complee VoIP Telecom Service Provider The Evoluion of a SIP Trunking Provider By: Sean Rivers Direcor of Technology parner Assurance 1 Agenda Who is Bandwidh.com Today Before VoIP The Addiion of VoIP

More information

The naive method discussed in Lecture 1 uses the most recent observations to forecast future values. That is, Y ˆ t + 1

The naive method discussed in Lecture 1 uses the most recent observations to forecast future values. That is, Y ˆ t + 1 Business Condiions & Forecasing Exponenial Smoohing LECTURE 2 MOVING AVERAGES AND EXPONENTIAL SMOOTHING OVERVIEW This lecure inroduces ime-series smoohing forecasing mehods. Various models are discussed,

More information

Appendix D Flexibility Factor/Margin of Choice Desktop Research

Appendix D Flexibility Factor/Margin of Choice Desktop Research Appendix D Flexibiliy Facor/Margin of Choice Deskop Research Cheshire Eas Council Cheshire Eas Employmen Land Review Conens D1 Flexibiliy Facor/Margin of Choice Deskop Research 2 Final Ocober 2012 \\GLOBAL.ARUP.COM\EUROPE\MANCHESTER\JOBS\200000\223489-00\4

More information

II.1. Debt reduction and fiscal multipliers. dbt da dpbal da dg. bal

II.1. Debt reduction and fiscal multipliers. dbt da dpbal da dg. bal Quarerly Repor on he Euro Area 3/202 II.. Deb reducion and fiscal mulipliers The deerioraion of public finances in he firs years of he crisis has led mos Member Saes o adop sizeable consolidaion packages.

More information

An Analysis of Adoption of Digital Health Records under Switching Costs

An Analysis of Adoption of Digital Health Records under Switching Costs 1 An Analysis of Adopion of Digial Healh Records under Swiching Coss November 2010 ZAFER D. OZDEMIR a JOHN M. BARRON b SUBHAJYOTI BANDYOPADHYAY c ozdemir@muohio.edu; barron@purdue.edu; shubho.bandyopadhyay@warringon.ufl.edu

More information

Task is a schedulable entity, i.e., a thread

Task is a schedulable entity, i.e., a thread Real-Time Scheduling Sysem Model Task is a schedulable eniy, i.e., a hread Time consrains of periodic ask T: - s: saring poin - e: processing ime of T - d: deadline of T - p: period of T Periodic ask T

More information

ANALYSIS AND COMPARISONS OF SOME SOLUTION CONCEPTS FOR STOCHASTIC PROGRAMMING PROBLEMS

ANALYSIS AND COMPARISONS OF SOME SOLUTION CONCEPTS FOR STOCHASTIC PROGRAMMING PROBLEMS ANALYSIS AND COMPARISONS OF SOME SOLUTION CONCEPTS FOR STOCHASTIC PROGRAMMING PROBLEMS R. Caballero, E. Cerdá, M. M. Muñoz and L. Rey () Deparmen of Applied Economics (Mahemaics), Universiy of Málaga,

More information

MEDDELANDEN FRÅN SVENSKA HANDELSHÖGSKOLAN SWEDISH SCHOOL OF ECONOMICS AND BUSINESS ADMINISTRATION WORKING PAPERS

MEDDELANDEN FRÅN SVENSKA HANDELSHÖGSKOLAN SWEDISH SCHOOL OF ECONOMICS AND BUSINESS ADMINISTRATION WORKING PAPERS MEDDELANDEN FRÅN SVENSKA HANDELSHÖGSKOLAN SWEDISH SCHOOL OF ECONOMICS AND BUSINESS ADMINISTRATION WORKING PAPERS 3 Jukka Liikanen, Paul Soneman & Oo Toivanen INTERGENERATIONAL EFFECTS IN THE DIFFUSION

More information

DETERMINISTIC INVENTORY MODEL FOR ITEMS WITH TIME VARYING DEMAND, WEIBULL DISTRIBUTION DETERIORATION AND SHORTAGES KUN-SHAN WU

DETERMINISTIC INVENTORY MODEL FOR ITEMS WITH TIME VARYING DEMAND, WEIBULL DISTRIBUTION DETERIORATION AND SHORTAGES KUN-SHAN WU Yugoslav Journal of Operaions Research 2 (22), Number, 6-7 DEERMINISIC INVENORY MODEL FOR IEMS WIH IME VARYING DEMAND, WEIBULL DISRIBUION DEERIORAION AND SHORAGES KUN-SHAN WU Deparmen of Bussines Adminisraion

More information

MODELING REGULATORY REGIMES FOR LAST-MILE BROADBAND CONNECTIONS IN A SINGLE-PROVIDER MARKET: A MULTI-MODEL APPROACH

MODELING REGULATORY REGIMES FOR LAST-MILE BROADBAND CONNECTIONS IN A SINGLE-PROVIDER MARKET: A MULTI-MODEL APPROACH MODELING REGULATORY REGIMES FOR LAST-MILE BROADBAND CONNECTIONS IN A SINGLE-PROVIDER MARKET: A MULTI-MODEL APPROACH Richard Curry, PhD Candidae London Business School, Regen s Park, London NW1 4SA, Unied

More information

Information Theoretic Evaluation of Change Prediction Models for Large-Scale Software

Information Theoretic Evaluation of Change Prediction Models for Large-Scale Software Informaion Theoreic Evaluaion of Change Predicion Models for Large-Scale Sofware Mina Askari School of Compuer Science Universiy of Waerloo Waerloo, Canada maskari@uwaerloo.ca Ric Hol School of Compuer

More information

Hedging with Forwards and Futures

Hedging with Forwards and Futures Hedging wih orwards and uures Hedging in mos cases is sraighforward. You plan o buy 10,000 barrels of oil in six monhs and you wish o eliminae he price risk. If you ake he buy-side of a forward/fuures

More information

The Greek financial crisis: growing imbalances and sovereign spreads. Heather D. Gibson, Stephan G. Hall and George S. Tavlas

The Greek financial crisis: growing imbalances and sovereign spreads. Heather D. Gibson, Stephan G. Hall and George S. Tavlas The Greek financial crisis: growing imbalances and sovereign spreads Heaher D. Gibson, Sephan G. Hall and George S. Tavlas The enry The enry of Greece ino he Eurozone in 2001 produced a dividend in he

More information

Chabot College Physics Lab RC Circuits Scott Hildreth

Chabot College Physics Lab RC Circuits Scott Hildreth Chabo College Physics Lab Circuis Sco Hildreh Goals: Coninue o advance your undersanding of circuis, measuring resisances, currens, and volages across muliple componens. Exend your skills in making breadboard

More information

C Fast-Dealing Property Trading Game C

C Fast-Dealing Property Trading Game C AGES 8+ C Fas-Dealing Propery Trading Game C Y Collecor s Ediion Original MONOPOLY Game Rules plus Special Rules for his Ediion. CONTENTS Game board, 6 Collecible okens, 28 Tile Deed cards, 16 Wha he Deuce?

More information

INTEREST RATE FUTURES AND THEIR OPTIONS: SOME PRICING APPROACHES

INTEREST RATE FUTURES AND THEIR OPTIONS: SOME PRICING APPROACHES INTEREST RATE FUTURES AND THEIR OPTIONS: SOME PRICING APPROACHES OPENGAMMA QUANTITATIVE RESEARCH Absrac. Exchange-raded ineres rae fuures and heir opions are described. The fuure opions include hose paying

More information

Working Paper No. 482. Net Intergenerational Transfers from an Increase in Social Security Benefits

Working Paper No. 482. Net Intergenerational Transfers from an Increase in Social Security Benefits Working Paper No. 482 Ne Inergeneraional Transfers from an Increase in Social Securiy Benefis By Li Gan Texas A&M and NBER Guan Gong Shanghai Universiy of Finance and Economics Michael Hurd RAND Corporaion

More information

Term Structure of Prices of Asian Options

Term Structure of Prices of Asian Options Term Srucure of Prices of Asian Opions Jirô Akahori, Tsuomu Mikami, Kenji Yasuomi and Teruo Yokoa Dep. of Mahemaical Sciences, Risumeikan Universiy 1-1-1 Nojihigashi, Kusasu, Shiga 525-8577, Japan E-mail:

More information

Network Effects, Pricing Strategies, and Optimal Upgrade Time in Software Provision.

Network Effects, Pricing Strategies, and Optimal Upgrade Time in Software Provision. Nework Effecs, Pricing Sraegies, and Opimal Upgrade Time in Sofware Provision. Yi-Nung Yang* Deparmen of Economics Uah Sae Universiy Logan, UT 84322-353 April 3, 995 (curren version Feb, 996) JEL codes:

More information

UNDERSTANDING THE DEATH BENEFIT SWITCH OPTION IN UNIVERSAL LIFE POLICIES. Nadine Gatzert

UNDERSTANDING THE DEATH BENEFIT SWITCH OPTION IN UNIVERSAL LIFE POLICIES. Nadine Gatzert UNDERSTANDING THE DEATH BENEFIT SWITCH OPTION IN UNIVERSAL LIFE POLICIES Nadine Gazer Conac (has changed since iniial submission): Chair for Insurance Managemen Universiy of Erlangen-Nuremberg Lange Gasse

More information

International Journal of Supply and Operations Management

International Journal of Supply and Operations Management Inernaional Journal of Supply and Operaions Managemen IJSOM May 05, Volume, Issue, pp 5-547 ISSN-Prin: 8-59 ISSN-Online: 8-55 wwwijsomcom An EPQ Model wih Increasing Demand and Demand Dependen Producion

More information

Distributing Human Resources among Software Development Projects 1

Distributing Human Resources among Software Development Projects 1 Disribuing Human Resources among Sofware Developmen Proecs Macario Polo, María Dolores Maeos, Mario Piaini and rancisco Ruiz Summary This paper presens a mehod for esimaing he disribuion of human resources

More information

Nikkei Stock Average Volatility Index Real-time Version Index Guidebook

Nikkei Stock Average Volatility Index Real-time Version Index Guidebook Nikkei Sock Average Volailiy Index Real-ime Version Index Guidebook Nikkei Inc. Wih he modificaion of he mehodology of he Nikkei Sock Average Volailiy Index as Nikkei Inc. (Nikkei) sars calculaing and

More information

A Note on Using the Svensson procedure to estimate the risk free rate in corporate valuation

A Note on Using the Svensson procedure to estimate the risk free rate in corporate valuation A Noe on Using he Svensson procedure o esimae he risk free rae in corporae valuaion By Sven Arnold, Alexander Lahmann and Bernhard Schwezler Ocober 2011 1. The risk free ineres rae in corporae valuaion

More information

Forecasting, Ordering and Stock- Holding for Erratic Demand

Forecasting, Ordering and Stock- Holding for Erratic Demand ISF 2002 23 rd o 26 h June 2002 Forecasing, Ordering and Sock- Holding for Erraic Demand Andrew Eaves Lancaser Universiy / Andalus Soluions Limied Inroducion Erraic and slow-moving demand Demand classificaion

More information

SPEC model selection algorithm for ARCH models: an options pricing evaluation framework

SPEC model selection algorithm for ARCH models: an options pricing evaluation framework Applied Financial Economics Leers, 2008, 4, 419 423 SEC model selecion algorihm for ARCH models: an opions pricing evaluaion framework Savros Degiannakis a, * and Evdokia Xekalaki a,b a Deparmen of Saisics,

More information

Establishing Prefabricated Wood I-Joist Composite EI

Establishing Prefabricated Wood I-Joist Composite EI July 008 Esablishing Prefabricaed Wood I- Composie EI INTRODUCTION Composie (glued/nailed) floors are common in boh residenial and commercial consrucion, and have been successfully designed by Prefabricaed

More information

Trading on Short-Term Information

Trading on Short-Term Information Trading on Shor-Term Informaion Preliminary version. Commens welcome Alexander Gümbel * Deparmen of Economics European Universiy Insiue Badia Fiesolana 5006 San Domenico di Fiesole (FI) Ialy e-mail: guembel@daacomm.iue.i

More information

Consumer Flexibility, Data Quality and Targeted Pricing

Consumer Flexibility, Data Quality and Targeted Pricing No 117 Consumer Flexibiliy, Daa Qualiy and Targeed Pricing Geza Sapi, Irina Suleymanova November 2013 IMPRINT DICE DISCUSSION PAPER Published by düsseldorf universiy press (dup) on behalf of Heinrich Heine

More information

Two Compartment Body Model and V d Terms by Jeff Stark

Two Compartment Body Model and V d Terms by Jeff Stark Two Comparmen Body Model and V d Terms by Jeff Sark In a one-comparmen model, we make wo imporan assumpions: (1) Linear pharmacokineics - By his, we mean ha eliminaion is firs order and ha pharmacokineic

More information

SELF-EVALUATION FOR VIDEO TRACKING SYSTEMS

SELF-EVALUATION FOR VIDEO TRACKING SYSTEMS SELF-EVALUATION FOR VIDEO TRACKING SYSTEMS Hao Wu and Qinfen Zheng Cenre for Auomaion Research Dep. of Elecrical and Compuer Engineering Universiy of Maryland, College Park, MD-20742 {wh2003, qinfen}@cfar.umd.edu

More information

Forecasting and Information Sharing in Supply Chains Under Quasi-ARMA Demand

Forecasting and Information Sharing in Supply Chains Under Quasi-ARMA Demand Forecasing and Informaion Sharing in Supply Chains Under Quasi-ARMA Demand Avi Giloni, Clifford Hurvich, Sridhar Seshadri July 9, 2009 Absrac In his paper, we revisi he problem of demand propagaion in

More information

DOES TRADING VOLUME INFLUENCE GARCH EFFECTS? SOME EVIDENCE FROM THE GREEK MARKET WITH SPECIAL REFERENCE TO BANKING SECTOR

DOES TRADING VOLUME INFLUENCE GARCH EFFECTS? SOME EVIDENCE FROM THE GREEK MARKET WITH SPECIAL REFERENCE TO BANKING SECTOR Invesmen Managemen and Financial Innovaions, Volume 4, Issue 3, 7 33 DOES TRADING VOLUME INFLUENCE GARCH EFFECTS? SOME EVIDENCE FROM THE GREEK MARKET WITH SPECIAL REFERENCE TO BANKING SECTOR Ahanasios

More information

Can Individual Investors Use Technical Trading Rules to Beat the Asian Markets?

Can Individual Investors Use Technical Trading Rules to Beat the Asian Markets? Can Individual Invesors Use Technical Trading Rules o Bea he Asian Markes? INTRODUCTION In radiional ess of he weak-form of he Efficien Markes Hypohesis, price reurn differences are found o be insufficien

More information

Modeling Stock Price Dynamics with Fuzzy Opinion Networks

Modeling Stock Price Dynamics with Fuzzy Opinion Networks Modeling Sock Price Dynamics wih Fuzzy Opinion Neworks Li-Xin Wang Deparmen of Auomaion Science and Technology Xian Jiaoong Universiy, Xian, P.R. China Email: lxwang@mail.xju.edu.cn Key words: Sock price

More information

The Interaction of Guarantees, Surplus Distribution, and Asset Allocation in With Profit Life Insurance Policies

The Interaction of Guarantees, Surplus Distribution, and Asset Allocation in With Profit Life Insurance Policies 1 The Ineracion of Guaranees, Surplus Disribuion, and Asse Allocaion in Wih Profi Life Insurance Policies Alexander Kling * Insiu für Finanz- und Akuarwissenschafen, Helmholzsr. 22, 89081 Ulm, Germany

More information

Price Controls and Banking in Emissions Trading: An Experimental Evaluation

Price Controls and Banking in Emissions Trading: An Experimental Evaluation This version: March 2014 Price Conrols and Banking in Emissions Trading: An Experimenal Evaluaion John K. Sranlund Deparmen of Resource Economics Universiy of Massachuses-Amhers James J. Murphy Deparmen

More information

Rationales of Mortgage Insurance Premium Structures

Rationales of Mortgage Insurance Premium Structures JOURNAL OF REAL ESTATE RESEARCH Raionales of Morgage Insurance Premium Srucures Barry Dennis* Chionglong Kuo* Tyler T. Yang* Absrac. This sudy examines he raionales for he design of morgage insurance premium

More information

SUBJECT SA0 OF THE INSTITUTE AND FACULTY OF ACTUARIES

SUBJECT SA0 OF THE INSTITUTE AND FACULTY OF ACTUARIES SUBJECT SA0 OF THE INSTITUTE AND FACULTY OF ACTUARIES Man On Wong Essay on Welfare Effecs of Developing Reverse Morgage Marke in China Subjec SA0 Advisors Bing Zheng Chen James Orr Prepared a School of

More information

Present Value Methodology

Present Value Methodology Presen Value Mehodology Econ 422 Invesmen, Capial & Finance Universiy of Washingon Eric Zivo Las updaed: April 11, 2010 Presen Value Concep Wealh in Fisher Model: W = Y 0 + Y 1 /(1+r) The consumer/producer

More information

µ r of the ferrite amounts to 1000...4000. It should be noted that the magnetic length of the + δ

µ r of the ferrite amounts to 1000...4000. It should be noted that the magnetic length of the + δ Page 9 Design of Inducors and High Frequency Transformers Inducors sore energy, ransformers ransfer energy. This is he prime difference. The magneic cores are significanly differen for inducors and high

More information

The option pricing framework

The option pricing framework Chaper 2 The opion pricing framework The opion markes based on swap raes or he LIBOR have become he larges fixed income markes, and caps (floors) and swapions are he mos imporan derivaives wihin hese markes.

More information

Predicting Stock Market Index Trading Signals Using Neural Networks

Predicting Stock Market Index Trading Signals Using Neural Networks Predicing Sock Marke Index Trading Using Neural Neworks C. D. Tilakarane, S. A. Morris, M. A. Mammadov, C. P. Hurs Cenre for Informaics and Applied Opimizaion School of Informaion Technology and Mahemaical

More information

One dictionary: Native language - English/English - native language or English - English

One dictionary: Native language - English/English - native language or English - English Faculy of Social Sciences School of Business Corporae Finance Examinaion December 03 English Dae: Monday 09 December, 03 Time: 4 hours/ 9:00-3:00 Toal number of pages including he cover page: 5 Toal number

More information

Research. Michigan. Center. Retirement. Behavioral Effects of Social Security Policies on Benefit Claiming, Retirement and Saving.

Research. Michigan. Center. Retirement. Behavioral Effects of Social Security Policies on Benefit Claiming, Retirement and Saving. Michigan Universiy of Reiremen Research Cener Working Paper WP 2012-263 Behavioral Effecs of Social Securiy Policies on Benefi Claiming, Reiremen and Saving Alan L. Gusman and Thomas L. Seinmeier M R R

More information

Depreciation and Corporate Taxes

Depreciation and Corporate Taxes 205 Depreciaion and Corporae Taxes Chris Hendrickson Carnegie Mellon Universiy Tung Au Carnegie Mellon Universiy 205.1 Depreciaion as Tax Deducion 205.2 Tax Laws and Tax Planning 205.3 Decision Crieria

More information

LECTURE: SOCIAL SECURITY HILARY HOYNES UC DAVIS EC230 OUTLINE OF LECTURE:

LECTURE: SOCIAL SECURITY HILARY HOYNES UC DAVIS EC230 OUTLINE OF LECTURE: LECTURE: SOCIAL SECURITY HILARY HOYNES UC DAVIS EC230 OUTLINE OF LECTURE: 1. Inroducion and definiions 2. Insiuional Deails in Social Securiy 3. Social Securiy and Redisribuion 4. Jusificaion for Governmen

More information

TSG-RAN Working Group 1 (Radio Layer 1) meeting #3 Nynashamn, Sweden 22 nd 26 th March 1999

TSG-RAN Working Group 1 (Radio Layer 1) meeting #3 Nynashamn, Sweden 22 nd 26 th March 1999 TSG-RAN Working Group 1 (Radio Layer 1) meeing #3 Nynashamn, Sweden 22 nd 26 h March 1999 RAN TSGW1#3(99)196 Agenda Iem: 9.1 Source: Tile: Documen for: Moorola Macro-diversiy for he PRACH Discussion/Decision

More information

A Further Examination of Insurance Pricing and Underwriting Cycles

A Further Examination of Insurance Pricing and Underwriting Cycles A Furher Examinaion of Insurance ricing and Underwriing Cycles AFIR Conference, Sepember 2005, Zurich, Swizerland Chris K. Madsen, GE Insurance Soluions, Copenhagen, Denmark Svend Haasrup, GE Insurance

More information

Optimal Stock Selling/Buying Strategy with reference to the Ultimate Average

Optimal Stock Selling/Buying Strategy with reference to the Ultimate Average Opimal Sock Selling/Buying Sraegy wih reference o he Ulimae Average Min Dai Dep of Mah, Naional Universiy of Singapore, Singapore Yifei Zhong Dep of Mah, Naional Universiy of Singapore, Singapore July

More information

Chapter Four: Methodology

Chapter Four: Methodology Chaper Four: Mehodology 1 Assessmen of isk Managemen Sraegy Comparing Is Cos of isks 1.1 Inroducion If we wan o choose a appropriae risk managemen sraegy, no only we should idenify he influence ha risks

More information

PATHWISE PROPERTIES AND PERFORMANCE BOUNDS FOR A PERISHABLE INVENTORY SYSTEM

PATHWISE PROPERTIES AND PERFORMANCE BOUNDS FOR A PERISHABLE INVENTORY SYSTEM PATHWISE PROPERTIES AND PERFORMANCE BOUNDS FOR A PERISHABLE INVENTORY SYSTEM WILLIAM L. COOPER Deparmen of Mechanical Engineering, Universiy of Minnesoa, 111 Church Sree S.E., Minneapolis, MN 55455 billcoop@me.umn.edu

More information

Improvement of a TCP Incast Avoidance Method for Data Center Networks

Improvement of a TCP Incast Avoidance Method for Data Center Networks Improvemen of a Incas Avoidance Mehod for Daa Cener Neworks Kazuoshi Kajia, Shigeyuki Osada, Yukinobu Fukushima and Tokumi Yokohira The Graduae School of Naural Science and Technology, Okayama Universiy

More information

The Impact of Surplus Distribution on the Risk Exposure of With Profit Life Insurance Policies Including Interest Rate Guarantees.

The Impact of Surplus Distribution on the Risk Exposure of With Profit Life Insurance Policies Including Interest Rate Guarantees. The Impac of Surplus Disribuion on he Risk Exposure of Wih Profi Life Insurance Policies Including Ineres Rae Guaranees Alexander Kling 1 Insiu für Finanz- und Akuarwissenschafen, Helmholzsraße 22, 89081

More information

Chapter 10 Social Security 1

Chapter 10 Social Security 1 Chaper 0 Social Securiy 0. Inroducion A ypical social securiy sysem provides income during periods of unemploymen, ill-healh or disabiliy, and financial suppor, in he form of pensions, o he reired. Alhough

More information