benefit is 2, paid if the policyholder dies within the year, and probability of death within the year is ).
|
|
- Lilian O’Brien’
- 8 years ago
- Views:
Transcription
1 REVIEW OF RISK MANAGEMENT CONCEPTS LOSS DISTRIBUTIONS AND INSURANCE Loss and nsurance: When someone s subject to the rsk of ncurrng a fnancal loss, the loss s generally modeled usng a random varable or some combnaton of random varables. The loss s often related to a partcular tme nterval - for example, an ndvdual may own property that mght suffer some damage durng the followng year. Someone who s at rsk of a fnancal loss may choose some form of nsurance protecton to reduce the mpact of the loss. An nsurance polcy s a contract between the party that s at rsk (the polcyholder) and an nsurer. Ths contract generally calls for the polcyholder to pay the nsurer some specfed amount, the nsurance premum, and n return, the nsurer wll remburse certan clams to the polcyholder. A clam s all or part of the loss that occurs, dependng on the nature of the nsurance contract. Modelng a loss random varable: There are a few ways of modelng a random loss/clam for a partcular nsurance polcy, dependng on the nature of the loss. Unless ndcated otherwse, we wll assume the amount pad to the polcyholder as a clam s the amount of the loss that occurs. Once the random varable representng the loss has been determned, the expected value of the loss,, µá s referred to as the pure premum for the polcy., µ s also the expected clam on the nsurer. Note that n general, mght be - t s possble that no loss occurs. The followng are the basc models used for descrbng the loss random varable. For a random varable a measure of the rsk s ~ = ]. The untzed rsk or coeffcent of varaton l = µ, µ for the random varable s defned to be ~. Models for descrbng a loss random varable : Case 1: The complete descrpton of s gven: In ths case, f s contnuous, the densty functon ²%³ or dstrbuton functon - ²%³ s gven. If s dscrete, the probablty functon (or possbly the dstrbuton functon) s gven. One typcal (and smple) example of the dscrete case s a loss random varable of the form ~F 2 wth probablty (ths mght arse n a one- year term lfe nsurance n whch the death wth probablty c beneft s 2, pad f the polcyholder des wthn the year, and probablty of death wthn the year s ). Another example of a dscrete loss random varable (wth more than two ponts) s the followng example of dental expenses for a famly over a one-year perod. 1
2 Amount of Dental Expense Probablty $ In some problems, all that s needed s the mean and varance of, and sometmes that s the only nformaton about that s gven (rather than the full descrpton of 's dstrbuton). Case 2: The probablty of a non-negatve loss s gven, and the condtonal dstrbuton ) of loss amount gven that a loss has occurred s gven: The probablty of no loss occurrng s c, and the loss amount s 0 f no loss occurs. Thus, 7 ~µ~c and ~) f a loss does occur. The random varable ) s the loss amount gven that a loss has occurred, so that ) s really the condtonal dstrbuton of the loss amount gven that a loss occurs. The random varable ) mght be descrbed n detal, or only the mean and varance of ) mght be gven. Note that f, )µ and = )µ are gven, then, ) µ ~ = )µ b ², )µ³ (ths s needed n the formulaton of = µ ).. We formulate as a "mxture" of two random varables, > and >, where > ~ s the constant random varable (not really random at all), and > ~ ), and wth weghts ~ c and ~. Then the frst two moments of are, µ~²c³, >µbh, >µ~h, )µ, snce, >µ~, and, µ~²c³, > µbh, > µ~h, ) µ. Then, = µ~h, ) µc²h, )µ³. For example, the loss due to fre damagng a partcular property mght be modeled ths way. Suppose that ~À s the probablty that fre damage occurs, and gven that fre damage occurs, the amount of damage, ), has a unform dstrbuton between $ Á and $ Á. Keep n mnd that ) s the loss amount gven that a loss has occurred, whereas s the ÁÁ uncondtonal loss amount. Then,, )µ ~ $ Á and, ) µ ~. Usng the formulas above, ÁÁ ÁÁ, µ ~ ²À³²Á ³ ~ $, and = µ ~ ²À³² ³ c ²³ ~. 2
3 Example 135: For a one-year dental nsurance polcy for a famly, we consder the followng two models for annual clams : () Amount of Dental Expense () Probablty $ () There s a probablty of Àthat no clam occurs, 7 ~µ~à, and f a clam occurs, the clam amount random varable ), has mean, )µ ~ À and varance = )µ ~ Á À. In each case, fnd, µ and = µ. Soluton: () In ths case the complete descrpton of s gven (Case 1 mentoned above)., µ ~ ²À³ b ²À³ b ²À³ b ²À³ b ²À³ ~ Á, µ ~ ²À³ b ²À³ b ²À³ b ²À³ b ²À³ ~ Á = µ ~ Á c ~ Á. () In ths case, the probablty of a clam occurrng s gven ² ~ À) along wth the mean and varance of the condtonal dstrbuton ) of clam amount gven that a clam occurs (Case 2 mentoned above)., µ ~ h, )µ ~ ²À³²À³ ~,, µ ~ h, ) µ ~ ²À³ = )µ b ², )µ³ µ ~ ²À³ Á À b ²À³ µ ~ Á À = µ ~, µ c ², µ³ ~ Á. Note that t s not a concdence that the mean and varance of turned out to be the same n () and (). Ths s true because the mean and varance of ) n () were chosen as the condtonal mean and varance of the dstrbuton n () gven that a clam occurs. Modelng the aggregate clams n a portfolo of nsurance polcesá The Indvdual Rsk Model The ndvdual rsk model assumes that the portfolo conssts of a specfc number, say, of nsurance polces, wth the clam for one perod on polcy beng the random varable (modeled n one of the ways descrbed above for an ndvdual polcy loss random varable). Unless mentoned otherwse, t s assumed that the 's are mutually ndependent random varables. Then the aggregate clam s the random varable : ~, wth, :µ ~, µ and = :µ ~ = µ. ~ ~ ~ 3
4 If, µ ~ and = µ ~ for each ~ Á Á ÀÀÀÁ, then the coeffcent of varaton of the l aggregate clam dstrbuton : s ~ ~, whch goes to 0 as SBÀ l = :µ = µ, : µ, µ l Example 136: An nsurer has a portfolo of 1000 one-year term lfe nsurance polces just ssued to 1000 dfferent (ndependent) ndvduals. Each polcy wll pay $1000 n the event that the polcyholder des wthn the year. For 500 of the polces, the probablty of death s.01 per polcyholder, and for the other 500 polces the probablty of death s.02 per polcyholder. Fnd the expected value and the standard devaton of the aggregate clam that the nsurer wll pay. Soluton: The aggregate clam random varable s :~, where s the clam from polcy. Then, :µ ~, µ and snce the clams are ndependent, ~ = :µ~ = µ. If s one of the 500 polces wth death probablty.01, then ~ F prob..99 prob. 01 ~ S, µ ~ ²À³ ~, = µ ~, µ c ², µ³ ~. If s one of the 500 polces wth death probablty.02, then, µ~á= µ~á. Thus,, :µ ~ ²³ b ²³ ~ Á Á = :µ ~ ²³ b ²Á ³ ~ Á Á S l = :µ ~ Á. ~ Example 137: Two portfolos of ndependent nsurance polces have the followng characterstcs: Portfolo A: Probablty Number of Clam Clam Class n Class per Polcy Amount 1 2, Portfolo B: Probablty Clam Amount Number of Clam Dstrbuton Class n Class per Polcy Mean Varance 1 2, The aggregate clams n the portfolos are denoted by : and :. = : µ = : µ ( Fnd. ) ( ) 4
5 Soluton: In ths example, nformaton s gven n the followng form: for polcy, the probablty of a clam occurrng s gven,, and the mean and varance of the condtonal dstrbuton of clam amount gven a clam occurs s gven,, ) µ ~, = ) µ ~. (Note that for each polcy n Portfolo (, = )µ~.) Then for polcy,, µ ~ h, ) µ, and = µ ~ ² c ³², ) µ³ b h = ) µ, and for a portfolo of ndependent polces,, :µ ~, µ and = :µ ~ = µ. For Portfolo (, any polcy n Class 1 has = µ ~ ²À ³²À ³² ³ b ²À ³²³ ~ À and any polcy n Class 2 has = µ ~ ²À³²À³² ³ b ²À³²³ ~ À, so that = : ( µ ~ ²À ³ b ²À³ ~. For Portfolo ), any polcy n Class 1 has = µ ~ ²À ³²À ³² ³ b ²À ³²³ ~ À and any polcy n Class 2 has = : µ ~ ²À ³ b ²À³ ~ = : ( µ Then, ~ À. ). = : µ ) = µ ~ ²À³²À³² ³ b ²À³²³ ~ À, so that The normal approxmaton to aggregate clams: For an aggregate clams dstrbuton :, f the mean and varance of : are known (, :µ and = :µ ), t s possble to approxmate probabltes for : by usng the normal dstrbuton. The 95-th percentle of aggregate clams s the number 8 for whch 7 : 8µ~À. If : s assumed to have a dstrbuton whch s approxmately normal, then by standardzng : we have :c, :µ 8c, :µ 8c, :µ = :µ = :µ = :µ l l l 7 : 8µ~7 µ~à, so that s equal to the 95-th percentle of the standard normal dstrbuton (whch s found to be when referrng to the standard normal table), so that 8 can be found. If the nsurer collects total premum of amount 8, then (assumng that t s reasonable to use the approxmaton) there s a 95% chance (approxmately) that aggregate clams wll be less than the premum collected, and there s a 5% chance that aggregate clams wll exceed the premum. Snce : s a sum of many ndependent ndvdual polcy loss random varables, the Central Lmt Theorem suggests that the normal approxmaton to : s not unreasonable. Relatve securty loadng: If the aggregate clam dstrbuton s :, wth mean, :µ, the total premum collected, say 8, can be wrtten n the form 8 ~ (1+ ) h, :µ. The factor s sometmes referred to as the relatve securty loadng contaned wthn the premum. The premum conssts of, :µ (expected aggregate clam) plus h, :µ, a loadng on top of the expected aggregate clam. 5
6 Example 138: An nsurance company provdes nsurance to three classes of ndependent nsureds wth the followng characterstcs: For Each Insured Number Probablty Expected Varance of Class n Class of a Clam Clam AmountClam Amount For each class, the amount of premum collected s ² b ³ (expected clams), where s the same for all three classes. Usng the normal approxmaton to aggregate clams, fnd so that the probablty that total clams exceed the amount of premum collected s.05. Soluton: We wsh to fnd 8~²b ³, :µ, so that 7 : 8µ~À, or equvalently, 7 : 8µ~À. Applyng the normal approxmaton and standardzng :, ths can be wrtten n the form :c, :µ 7 : 8µ~7 8c, :µ µ~à, so that 8c, :µ µ~à (the 95-th percentle of l l l = :µ = :µ = :µ the standard normal dstrbuton). Thus, once, :µ and = :µ are found, we can fnd 8~²b ³, :µ, and then fnd., :µ ~ ', µ ~ ' h, ) µ ~ ²À ³² ³ b ²À³²³ b ²À ³² ³ ~, snce there are 500 polces n class 1, each wth expected clam ²À ³² ³, and smlarly for classes 2 and 3. The polces are ndependent so that the varance of the sum of all polcy clams s the sum of the varances (no covarances when ndependence s assumed). The varance of clam for a polcy from class 1 s ² c ³ h ², )µ³ b h = )µ ~ ²À ³²À ³² ³ b ²À ³² ³, and there are 500 of those polces, and smlarly for classes 2 and 3. = :µ ~ ' = µ ~ ' ² c ³ h ², ) µ³ b h = ) µ µ ~ ²À ³²À ³² ³ b ²À ³² ³µ b ²À³²À³² ³ b ²À³²³µ b ²À ³²À ³² ³ b ²À ³² ³µ ~ Á À. Then, 8 ~ À~, and À. Note that s the relatve securty loadng. Mxture of Loss Dstrbutons 6
7 A portfolo of polces mght consst of two or more classes of polcyholder, as n the prevous example. In the prevous example, the number of polces n each class was known. It may be possble that the number of polces n each class s not known but the proporton of polces n each class s known. In such a stuaton, we mght be asked to descrbe the dstrbuton of the loss for a randomly chosen polcy from the portfolo of polces. The followng example llustrates ths dea. Example 139: The nsurer of a portfolo of automoble nsurance polces classfes each polcy as ether hgh rsk, medum rsk or low rsk. The portfolo conssts of 10% hgh rsk, 30% medum rsk and 60% low rsk polces. The clam means and varances for the three rsk classes are mean varance hgh rsk medum rsk 4 4 low rsk 1 1 A polcy s chosen at random from the portfolo. Fnd the mean and varance of ths polcy. Soluton: The dstrbuton of the randomly chosen polcy s the mxture of the three rsk class clam dstrbutons, usng the percentages as the mxng factors. If denotes the clam for the randomly chosen polcy, then all moments of (pdf and cdf also) are the weghted averages of the moments for the component dstrbutons n the mxture., µ ~ ²À³²³ b ²À³²³ b ²À³²³ ~ À s the mean. Snce = µ ~, µ c ², µ³, we need, µ n order to fnd the varance of. Let / denote the clam random varable for a hgh rsk polcy. Then ~ = / µ ~, µ c ², / µ³ ~, µ c ²³, from whch we get, µ ~ À / / / In a smlar way we get, µ~b²³ ~ and, µ~b²³ ~. Then 4 3, µ ~ ²À³²³ b ²À³²³ b ²À³²³ ~ À = µ ~ À c ²À³ ~ À. Note that the varance of s not the weghted average of the varances of /, 4 and 3., and Partal nsurance coverage: It s possble to construct an nsurance polcy n whch the clam pad by the nsurer s part, but not necessarly all, of the loss that occurs. There are a few standard types of partal nsurance coverage on a basc ground up loss random varable. () Excess-of-loss nsurance: An excess-of-loss nsurance specfes a deductble amount, say. If a loss of amount occurs, the nsurer pays nothng f the loss s less than, and pays the polcyholder the amount of the loss n excess of f the loss s greater than. The amount pad F f c f by the nsurer can be descrbed ~ ~ 4% c Á ¹. 7
8 The expected payment made by the nsurer per loss would be B ²% c ³ ²%³ % B n the contnuous case. Wth ntegraton by parts, ths can be shown to be equal to c- ²%³µ %. Two varatons on the noton of deductble are (a) the franchse deductble: a franchse deductble of amount refers to the stuaton n whch the nsurer pays 0 f the loss s below but pays the full amount of loss f the loss s above ; the amount pad by the nsurer can be descrbed as F f f (b) the dsappearng deductble: a dsappearng deductble wth lower lmt and Z Z upper lmt (where ) refers to the stuaton n whch the nsurer pays 0 f the loss s below, the nsurer pays the full loss f the loss amount s above Z, and the deductble amount reduces lnearly from to 0 as the loss ncreases from to Z ; the amount pad by Z the nsurer can be descrbed as c Z J h Z c Z. Example 140: A dscrete loss random varable has the followng two-pont dstrbuton: 7 ~µ~7 ~µ~à. An excess-of-loss nsurance polcy s set up for ths loss, wth deductble. It s found that the expected clam on the nsurer s. f c f Soluton: The excess-of-loss clam on the nsurer s. We proceed by "tral-and-error". Suppose our ntal "guess" s that. Then the clam on the nsurer wll be ether c or c, each wth probablty À. so that the expected clam on the nsurer wll be ² c ³²À ³ b ² c ³²À ³ ~, whch mples that ~À. Ths contradcts our "guess" that. Ths ndcates that the guess was wrong. Thus,, so that the clam on the nsurer wll be (f ~) or c, each wth probablty À. The expected clam on the nsurer wll then be ² c ³²À ³ ~ S ~. () Polcy lmt: A polcy lmt of amount " ndcates that the nsurer wll pay a maxmum amount of " on a clam. Therefore, the amount pad by the nsurer s F f ". " f " " The expected payment made by the nsurer per loss would be %h ²%³%b"h c- ²"³µ n the contnuous case. Ths can be shown to be equal to c- ²%³µ %. " It s possble to combne an excess-of-loss partal nsurance wth a polcy lmt. If a polcy has a deductble of and a lmt of ", then the clam amount pad by the nsurer can be descrbed as 8
9 f H cf ". Note that "the deductble s appled after the polcy s appled". "c f " Ths means that a loss of amount greater than " trggers the polcy lmt of amount ", and then the deductble s appled to that lmt, resultng n a payment by the nsurer of amount "c. The expected payment made by the nsurer per loss would be " ²%c³h ²%³%b²"c³h c- ²"³µ n the contnuous case. Ths can be shown to be equal to c- ²%³µ %. " A varaton on the noton of polcy lmt s the maxmum clam amount, say nsurer pays the clam up to a maxmum amount of nsurance cap. An nsurance cap specfes a, that would be pad f a loss occurs on the polcy, so that the. If there s no deductble, ths s the same as a polcy lmt, but f there s a deductble of, then the maxmum amount pad by the nsurer s ~"c. In ths case, the polcy lmt of amount " s the same as an nsurance cap of amount "c. () Proportonal nsurance - Proportonal nsurance specfes a fracton ( ), and f a loss of amount occurs, the nsurer pays the polcyholder Á the specfed fracton of the full loss. When there are lmts on the amount pad by the nsurer (such as deductble, polcy lmt, etc.), t s possble to consder two random varables related to the basc ground up loss. The random s the amount pad per loss, and the random s the amount pad per payment made. If there s a deductble of Á the random wll be 0 f, ~ c f. The random s the condtonal random varable of amount pad gven that a payment s made. If there s a deductble of, ~ c f. If the pdf of s ²%³, and there s a deductble of and a polcy lmt of ", then the pdf's can be expressed n terms of the pdf of. - ²³ & ~ ²% ³ ²&b³ & "c² % E²&³ ~ J, and c - ²"³ & ~ " c ²% "³ & "c 9
10 ²&³ J ²&b³ c- ²³ c- ²"³ c- ²³ 0 &"c(densty) &~"c(a pont of probablty). & "c Example 141: For a certan nsurance, ndvdual losses last year were unformly dstrbuted over the nterval ²Á ³. A deductble of 100 s appled to each loss (the nsurer pays the loss n excess of the deductble of 100). Ths year, ndvdual losses are unformly dstrbuted over the nterval ²Á ³ and a deductble of 100 s stll appled. Determne the percentage ncrease n the expected amount pad by the nsurer from last year to ths year. Also, for last year, fnd the pdf of the amount pad per loss, and fnd the pdf of the amount pad per payment. Soluton: Last year, for a loss of amount, the amount pad by the nsurer was F f c ~. Last year the p.d.f. of the loss random varable was ²%³ ~ (unform dstrbuton on the nterval ²Á ³ by the nsurer last year was ²% c ³ h % ~ À Ths year, for a loss of amount, the amount pad by the nsurer s stll F f c f ). The expected ~, but ths year the p.d.f. of the loss random varable s ²%³ ~ (unform dstrbuton on the nterval ²Á ³ by the nsurer ths year s ²% c ³ h % ~ À À À The percentage ncrease s ² c ³ ~ À. The pdf of the amount pad per loss last year s À & ~ ²% ³ ²&³ E H À & ² % ³, and 0 otherwse. Note µ ~ ²À³²³ b & h ²À³ & ~. ). The expected payment The pdf of the amount pad per payment last year s ²&b³ ²&b³ À ²&³ ~ ~ ~ ~ for & ( % c- ²³ c- ²³ µ µ & h ² ³ & ~ ~ À ~ c- ²³ and 0 otherwse. Note that s the expected amount pad per payment made. Rensurance: In order to lmt the exposure to catastrophc clams that can occur, nsurers often set up rensurance arrangements wth other nsurers. The basc forms of rensurance are very smlar algebracally to the partal nsurances on ndvdual polces descrbed above, but they apply to the nsurer's aggregate clam random varable :. The clams pad by the cedng nsurer (the nsurer who purchases the rensurance) are referred to as retaned clams. 10
11 () Stop-loss rensurance - A stop-loss rensurance specfes a deductble amount. If the aggregate clam : s less than then the rensurer pays nothng, but f the aggregate clam s greater than then the rensurer pays the aggregate clam n excess of. F f : :c f : The amount pad by the rensurer can be descrbed as. () Rensurance cap - A rensurance cap specfes a maxmum amount pad by the rensurer, say. Ths would usually be set up n conjuncton wth a stop-loss wth deductble. In that case. the clam pad by the rensurer can be descrbed as f : H :cf : b f : b Notce that ths stop-loss rensurance wth a deductble of and a cap of s algebracally equal to a stop loss polcy wth deductble mnus a stop-loss polcy wth a deductble of b. () Proportonal rensurance - Proportonal rensurance specfes a fracton ( ), and f aggregate clams of amount : occur, the rensurer pays :Á and the cedng nsurer pays ² c ³:. Example 142: A lfe nsurance company covers 16,000 mutually ndependent lves for 1-year term lfe nsurance: Beneft Number Probablty Class Amount Covered of Clam The nsurance company's retenton lmt s 2 unts per lfe. Rensurance s purchased for 0.03 per unt. The cedng nsurer collects a premum of 8~, :µb l= :µb9, where : denotes the dstrbuton of retaned clams and 9 s the cost of rensurance. Fnd 8. Soluton: The cedng nsurer wll cover all clams from classes 1 and 2, and wll cover the frst 2 unts of clam from any polcy n class 3. The cedng nsurer purchases 2 unts of rensurance for each of the polces wth beneft amount 4, for a total of ²³ ~ unts rensured. The cost of the rensurance s 9 ~ ²À³ ~. The retaned clam dstrbuton : conssts of 8000 (Class 1) polces wth ~ À and, ) µ ~ and 8000 polces ( b, Classes 2 and 3 combned) wth ~ À and, )µ~. We are usng the notaton mentoned earler, ) s the condtonal clam from polcy 11
12 gven that a clam occurs. Then, s related to ) through the relatonshps, µ~, )µ and = µ~²c³², )µ³ b h= )µ. In ths case = )µ~ for all polces - ths s generally assumed for term lfe nsurances. Then,, :µ ~, µ ~ ²À ³²³ b ²À ³²³ ~ and = :µ ~ = µ ~ ²À ³²À ³² ³ b ²À ³²À ³² ³ ~. Then, 8 ~ b l b ~ À. 12
THE DISTRIBUTION OF LOAN PORTFOLIO VALUE * Oldrich Alfons Vasicek
HE DISRIBUION OF LOAN PORFOLIO VALUE * Oldrch Alfons Vascek he amount of captal necessary to support a portfolo of debt securtes depends on the probablty dstrbuton of the portfolo loss. Consder a portfolo
More informationThe OC Curve of Attribute Acceptance Plans
The OC Curve of Attrbute Acceptance Plans The Operatng Characterstc (OC) curve descrbes the probablty of acceptng a lot as a functon of the lot s qualty. Fgure 1 shows a typcal OC Curve. 10 8 6 4 1 3 4
More informationTraffic-light a stress test for life insurance provisions
MEMORANDUM Date 006-09-7 Authors Bengt von Bahr, Göran Ronge Traffc-lght a stress test for lfe nsurance provsons Fnansnspetonen P.O. Box 6750 SE-113 85 Stocholm [Sveavägen 167] Tel +46 8 787 80 00 Fax
More informationTraffic-light extended with stress test for insurance and expense risks in life insurance
PROMEMORIA Datum 0 July 007 FI Dnr 07-1171-30 Fnansnspetonen Författare Bengt von Bahr, Göran Ronge Traffc-lght extended wth stress test for nsurance and expense rss n lfe nsurance Summary Ths memorandum
More informationCHAPTER 14 MORE ABOUT REGRESSION
CHAPTER 14 MORE ABOUT REGRESSION We learned n Chapter 5 that often a straght lne descrbes the pattern of a relatonshp between two quanttatve varables. For nstance, n Example 5.1 we explored the relatonshp
More informationHedging Interest-Rate Risk with Duration
FIXED-INCOME SECURITIES Chapter 5 Hedgng Interest-Rate Rsk wth Duraton Outlne Prcng and Hedgng Prcng certan cash-flows Interest rate rsk Hedgng prncples Duraton-Based Hedgng Technques Defnton of duraton
More informationStress test for measuring insurance risks in non-life insurance
PROMEMORIA Datum June 01 Fnansnspektonen Författare Bengt von Bahr, Younes Elonq and Erk Elvers Stress test for measurng nsurance rsks n non-lfe nsurance Summary Ths memo descrbes stress testng of nsurance
More informationWhat is Candidate Sampling
What s Canddate Samplng Say we have a multclass or mult label problem where each tranng example ( x, T ) conssts of a context x a small (mult)set of target classes T out of a large unverse L of possble
More informationDEFINING %COMPLETE IN MICROSOFT PROJECT
CelersSystems DEFINING %COMPLETE IN MICROSOFT PROJECT PREPARED BY James E Aksel, PMP, PMI-SP, MVP For Addtonal Informaton about Earned Value Management Systems and reportng, please contact: CelersSystems,
More informationPSYCHOLOGICAL RESEARCH (PYC 304-C) Lecture 12
14 The Ch-squared dstrbuton PSYCHOLOGICAL RESEARCH (PYC 304-C) Lecture 1 If a normal varable X, havng mean µ and varance σ, s standardsed, the new varable Z has a mean 0 and varance 1. When ths standardsed
More informationExtending Probabilistic Dynamic Epistemic Logic
Extendng Probablstc Dynamc Epstemc Logc Joshua Sack May 29, 2008 Probablty Space Defnton A probablty space s a tuple (S, A, µ), where 1 S s a set called the sample space. 2 A P(S) s a σ-algebra: a set
More information1 Example 1: Axis-aligned rectangles
COS 511: Theoretcal Machne Learnng Lecturer: Rob Schapre Lecture # 6 Scrbe: Aaron Schld February 21, 2013 Last class, we dscussed an analogue for Occam s Razor for nfnte hypothess spaces that, n conjuncton
More informationNPAR TESTS. One-Sample Chi-Square Test. Cell Specification. Observed Frequencies 1O i 6. Expected Frequencies 1EXP i 6
PAR TESTS If a WEIGHT varable s specfed, t s used to replcate a case as many tmes as ndcated by the weght value rounded to the nearest nteger. If the workspace requrements are exceeded and samplng has
More informationLuby s Alg. for Maximal Independent Sets using Pairwise Independence
Lecture Notes for Randomzed Algorthms Luby s Alg. for Maxmal Independent Sets usng Parwse Independence Last Updated by Erc Vgoda on February, 006 8. Maxmal Independent Sets For a graph G = (V, E), an ndependent
More informationUnderwriting Risk. Glenn Meyers. Insurance Services Office, Inc.
Underwrtng Rsk By Glenn Meyers Insurance Servces Offce, Inc. Abstract In a compettve nsurance market, nsurers have lmted nfluence on the premum charged for an nsurance contract. hey must decde whether
More informationVasicek s Model of Distribution of Losses in a Large, Homogeneous Portfolio
Vascek s Model of Dstrbuton of Losses n a Large, Homogeneous Portfolo Stephen M Schaefer London Busness School Credt Rsk Electve Summer 2012 Vascek s Model Important method for calculatng dstrbuton of
More informationAn Alternative Way to Measure Private Equity Performance
An Alternatve Way to Measure Prvate Equty Performance Peter Todd Parlux Investment Technology LLC Summary Internal Rate of Return (IRR) s probably the most common way to measure the performance of prvate
More informationRecurrence. 1 Definitions and main statements
Recurrence 1 Defntons and man statements Let X n, n = 0, 1, 2,... be a MC wth the state space S = (1, 2,...), transton probabltes p j = P {X n+1 = j X n = }, and the transton matrx P = (p j ),j S def.
More informationAnalysis of Premium Liabilities for Australian Lines of Business
Summary of Analyss of Premum Labltes for Australan Lnes of Busness Emly Tao Honours Research Paper, The Unversty of Melbourne Emly Tao Acknowledgements I am grateful to the Australan Prudental Regulaton
More informationCHAPTER 5 RELATIONSHIPS BETWEEN QUANTITATIVE VARIABLES
CHAPTER 5 RELATIONSHIPS BETWEEN QUANTITATIVE VARIABLES In ths chapter, we wll learn how to descrbe the relatonshp between two quanttatve varables. Remember (from Chapter 2) that the terms quanttatve varable
More informationLecture 3: Force of Interest, Real Interest Rate, Annuity
Lecture 3: Force of Interest, Real Interest Rate, Annuty Goals: Study contnuous compoundng and force of nterest Dscuss real nterest rate Learn annuty-mmedate, and ts present value Study annuty-due, and
More informationMethods for Calculating Life Insurance Rates
World Appled Scences Journal 5 (4): 653-663, 03 ISSN 88-495 IDOSI Pulcatons, 03 DOI: 0.589/dos.wasj.03.5.04.338 Methods for Calculatng Lfe Insurance Rates Madna Movsarovna Magomadova Chechen State Unversty,
More informationCan Auto Liability Insurance Purchases Signal Risk Attitude?
Internatonal Journal of Busness and Economcs, 2011, Vol. 10, No. 2, 159-164 Can Auto Lablty Insurance Purchases Sgnal Rsk Atttude? Chu-Shu L Department of Internatonal Busness, Asa Unversty, Tawan Sheng-Chang
More informationCHOLESTEROL REFERENCE METHOD LABORATORY NETWORK. Sample Stability Protocol
CHOLESTEROL REFERENCE METHOD LABORATORY NETWORK Sample Stablty Protocol Background The Cholesterol Reference Method Laboratory Network (CRMLN) developed certfcaton protocols for total cholesterol, HDL
More informationv a 1 b 1 i, a 2 b 2 i,..., a n b n i.
SECTION 8.4 COMPLEX VECTOR SPACES AND INNER PRODUCTS 455 8.4 COMPLEX VECTOR SPACES AND INNER PRODUCTS All the vector spaces we have studed thus far n the text are real vector spaces snce the scalars are
More information1. Measuring association using correlation and regression
How to measure assocaton I: Correlaton. 1. Measurng assocaton usng correlaton and regresson We often would lke to know how one varable, such as a mother's weght, s related to another varable, such as a
More informationSection 5.4 Annuities, Present Value, and Amortization
Secton 5.4 Annutes, Present Value, and Amortzaton Present Value In Secton 5.2, we saw that the present value of A dollars at nterest rate per perod for n perods s the amount that must be deposted today
More informationHow To Calculate The Accountng Perod Of Nequalty
Inequalty and The Accountng Perod Quentn Wodon and Shlomo Ytzha World Ban and Hebrew Unversty September Abstract Income nequalty typcally declnes wth the length of tme taen nto account for measurement.
More informationCausal, Explanatory Forecasting. Analysis. Regression Analysis. Simple Linear Regression. Which is Independent? Forecasting
Causal, Explanatory Forecastng Assumes cause-and-effect relatonshp between system nputs and ts output Forecastng wth Regresson Analyss Rchard S. Barr Inputs System Cause + Effect Relatonshp The job of
More information) of the Cell class is created containing information about events associated with the cell. Events are added to the Cell instance
Calbraton Method Instances of the Cell class (one nstance for each FMS cell) contan ADC raw data and methods assocated wth each partcular FMS cell. The calbraton method ncludes event selecton (Class Cell
More informationStatistical Methods to Develop Rating Models
Statstcal Methods to Develop Ratng Models [Evelyn Hayden and Danel Porath, Österrechsche Natonalbank and Unversty of Appled Scences at Manz] Source: The Basel II Rsk Parameters Estmaton, Valdaton, and
More informationCalculation of Sampling Weights
Perre Foy Statstcs Canada 4 Calculaton of Samplng Weghts 4.1 OVERVIEW The basc sample desgn used n TIMSS Populatons 1 and 2 was a two-stage stratfed cluster desgn. 1 The frst stage conssted of a sample
More informationLoss analysis of a life insurance company applying discrete-time risk-minimizing hedging strategies
Insurance: Mathematcs and Economcs 42 2008 1035 1049 www.elsever.com/locate/me Loss analyss of a lfe nsurance company applyng dscrete-tme rsk-mnmzng hedgng strateges An Chen Netspar, he Netherlands Department
More information1 De nitions and Censoring
De ntons and Censorng. Survval Analyss We begn by consderng smple analyses but we wll lead up to and take a look at regresson on explanatory factors., as n lnear regresson part A. The mportant d erence
More informationTHE METHOD OF LEAST SQUARES THE METHOD OF LEAST SQUARES
The goal: to measure (determne) an unknown quantty x (the value of a RV X) Realsaton: n results: y 1, y 2,..., y j,..., y n, (the measured values of Y 1, Y 2,..., Y j,..., Y n ) every result s encumbered
More informationCredit Limit Optimization (CLO) for Credit Cards
Credt Lmt Optmzaton (CLO) for Credt Cards Vay S. Desa CSCC IX, Ednburgh September 8, 2005 Copyrght 2003, SAS Insttute Inc. All rghts reserved. SAS Propretary Agenda Background Tradtonal approaches to credt
More information8.5 UNITARY AND HERMITIAN MATRICES. The conjugate transpose of a complex matrix A, denoted by A*, is given by
6 CHAPTER 8 COMPLEX VECTOR SPACES 5. Fnd the kernel of the lnear transformaton gven n Exercse 5. In Exercses 55 and 56, fnd the mage of v, for the ndcated composton, where and are gven by the followng
More informationEstimating Total Claim Size in the Auto Insurance Industry: a Comparison between Tweedie and Zero-Adjusted Inverse Gaussian Distribution
Estmatng otal Clam Sze n the Auto Insurance Industry: a Comparson between weede and Zero-Adjusted Inverse Gaussan Dstrbuton Autora: Adrana Bruscato Bortoluzzo, Italo De Paula Franca, Marco Antono Leonel
More informationStaff Paper. Farm Savings Accounts: Examining Income Variability, Eligibility, and Benefits. Brent Gloy, Eddy LaDue, and Charles Cuykendall
SP 2005-02 August 2005 Staff Paper Department of Appled Economcs and Management Cornell Unversty, Ithaca, New York 14853-7801 USA Farm Savngs Accounts: Examnng Income Varablty, Elgblty, and Benefts Brent
More informationPrediction of Disability Frequencies in Life Insurance
Predcton of Dsablty Frequences n Lfe Insurance Bernhard Köng Fran Weber Maro V. Wüthrch October 28, 2011 Abstract For the predcton of dsablty frequences, not only the observed, but also the ncurred but
More informationThe Development of Web Log Mining Based on Improve-K-Means Clustering Analysis
The Development of Web Log Mnng Based on Improve-K-Means Clusterng Analyss TngZhong Wang * College of Informaton Technology, Luoyang Normal Unversty, Luoyang, 471022, Chna wangtngzhong2@sna.cn Abstract.
More informationOn some special nonlevel annuities and yield rates for annuities
On some specal nonlevel annutes and yeld rates for annutes 1 Annutes wth payments n geometrc progresson 2 Annutes wth payments n Arthmetc Progresson 1 Annutes wth payments n geometrc progresson 2 Annutes
More informationA DYNAMIC CRASHING METHOD FOR PROJECT MANAGEMENT USING SIMULATION-BASED OPTIMIZATION. Michael E. Kuhl Radhamés A. Tolentino-Peña
Proceedngs of the 2008 Wnter Smulaton Conference S. J. Mason, R. R. Hll, L. Mönch, O. Rose, T. Jefferson, J. W. Fowler eds. A DYNAMIC CRASHING METHOD FOR PROJECT MANAGEMENT USING SIMULATION-BASED OPTIMIZATION
More informationSIMPLE LINEAR CORRELATION
SIMPLE LINEAR CORRELATION Smple lnear correlaton s a measure of the degree to whch two varables vary together, or a measure of the ntensty of the assocaton between two varables. Correlaton often s abused.
More informationUsing Series to Analyze Financial Situations: Present Value
2.8 Usng Seres to Analyze Fnancal Stuatons: Present Value In the prevous secton, you learned how to calculate the amount, or future value, of an ordnary smple annuty. The amount s the sum of the accumulated
More informationPERRON FROBENIUS THEOREM
PERRON FROBENIUS THEOREM R. CLARK ROBINSON Defnton. A n n matrx M wth real entres m, s called a stochastc matrx provded () all the entres m satsfy 0 m, () each of the columns sum to one, m = for all, ()
More informationTuition Fee Loan application notes
Tuton Fee Loan applcaton notes for new part-tme EU students 2012/13 About these notes These notes should be read along wth your Tuton Fee Loan applcaton form. The notes are splt nto three parts: Part 1
More informationTraffic State Estimation in the Traffic Management Center of Berlin
Traffc State Estmaton n the Traffc Management Center of Berln Authors: Peter Vortsch, PTV AG, Stumpfstrasse, D-763 Karlsruhe, Germany phone ++49/72/965/35, emal peter.vortsch@ptv.de Peter Möhl, PTV AG,
More informationModule 2 LOSSLESS IMAGE COMPRESSION SYSTEMS. Version 2 ECE IIT, Kharagpur
Module LOSSLESS IMAGE COMPRESSION SYSTEMS Lesson 3 Lossless Compresson: Huffman Codng Instructonal Objectves At the end of ths lesson, the students should be able to:. Defne and measure source entropy..
More informationTo manage leave, meeting institutional requirements and treating individual staff members fairly and consistently.
Corporate Polces & Procedures Human Resources - Document CPP216 Leave Management Frst Produced: Current Verson: Past Revsons: Revew Cycle: Apples From: 09/09/09 26/10/12 09/09/09 3 years Immedately Authorsaton:
More informationHow To Find The Dsablty Frequency Of A Clam
1 Predcton of Dsablty Frequences n Lfe Insurance Bernhard Köng 1, Fran Weber 1, Maro V. Wüthrch 2 Abstract: For the predcton of dsablty frequences, not only the observed, but also the ncurred but not yet
More informationADVERSE SELECTION IN INSURANCE MARKETS: POLICYHOLDER EVIDENCE FROM THE U.K. ANNUITY MARKET *
ADVERSE SELECTION IN INSURANCE MARKETS: POLICYHOLDER EVIDENCE FROM THE U.K. ANNUITY MARKET * Amy Fnkelsten Harvard Unversty and NBER James Poterba MIT and NBER * We are grateful to Jeffrey Brown, Perre-Andre
More informationTime Value of Money. Types of Interest. Compounding and Discounting Single Sums. Page 1. Ch. 6 - The Time Value of Money. The Time Value of Money
Ch. 6 - The Tme Value of Money Tme Value of Money The Interest Rate Smple Interest Compound Interest Amortzng a Loan FIN21- Ahmed Y, Dasht TIME VALUE OF MONEY OR DISCOUNTED CASH FLOW ANALYSIS Very Important
More informationRisk-based Fatigue Estimate of Deep Water Risers -- Course Project for EM388F: Fracture Mechanics, Spring 2008
Rsk-based Fatgue Estmate of Deep Water Rsers -- Course Project for EM388F: Fracture Mechancs, Sprng 2008 Chen Sh Department of Cvl, Archtectural, and Envronmental Engneerng The Unversty of Texas at Austn
More informationCourse outline. Financial Time Series Analysis. Overview. Data analysis. Predictive signal. Trading strategy
Fnancal Tme Seres Analyss Patrck McSharry patrck@mcsharry.net www.mcsharry.net Trnty Term 2014 Mathematcal Insttute Unversty of Oxford Course outlne 1. Data analyss, probablty, correlatons, vsualsaton
More informationOPTIMAL INVESTMENT POLICIES FOR THE HORSE RACE MODEL. Thomas S. Ferguson and C. Zachary Gilstein UCLA and Bell Communications May 1985, revised 2004
OPTIMAL INVESTMENT POLICIES FOR THE HORSE RACE MODEL Thomas S. Ferguson and C. Zachary Glsten UCLA and Bell Communcatons May 985, revsed 2004 Abstract. Optmal nvestment polces for maxmzng the expected
More informationFixed income risk attribution
5 Fxed ncome rsk attrbuton Chthra Krshnamurth RskMetrcs Group chthra.krshnamurth@rskmetrcs.com We compare the rsk of the actve portfolo wth that of the benchmark and segment the dfference between the two
More informationEstimating Total Claim Size in the Auto Insurance Industry: a Comparison between Tweedie and Zero-Adjusted Inverse Gaussian Distribution
Avalable onlne at http:// BAR, Curtba, v. 8, n. 1, art. 3, pp. 37-47, Jan./Mar. 2011 Estmatng Total Clam Sze n the Auto Insurance Industry: a Comparson between Tweede and Zero-Adjusted Inverse Gaussan
More informationEfficient Striping Techniques for Variable Bit Rate Continuous Media File Servers æ
Effcent Strpng Technques for Varable Bt Rate Contnuous Meda Fle Servers æ Prashant J. Shenoy Harrck M. Vn Department of Computer Scence, Department of Computer Scences, Unversty of Massachusetts at Amherst
More informationForecasting the Direction and Strength of Stock Market Movement
Forecastng the Drecton and Strength of Stock Market Movement Jngwe Chen Mng Chen Nan Ye cjngwe@stanford.edu mchen5@stanford.edu nanye@stanford.edu Abstract - Stock market s one of the most complcated systems
More informationSmall pots lump sum payment instruction
For customers Small pots lump sum payment nstructon Please read these notes before completng ths nstructon About ths nstructon Use ths nstructon f you re an ndvdual wth Aegon Retrement Choces Self Invested
More informationEfficient Project Portfolio as a tool for Enterprise Risk Management
Effcent Proect Portfolo as a tool for Enterprse Rsk Management Valentn O. Nkonov Ural State Techncal Unversty Growth Traectory Consultng Company January 5, 27 Effcent Proect Portfolo as a tool for Enterprse
More informationTransition Matrix Models of Consumer Credit Ratings
Transton Matrx Models of Consumer Credt Ratngs Abstract Although the corporate credt rsk lterature has many studes modellng the change n the credt rsk of corporate bonds over tme, there s far less analyss
More information1.2 DISTRIBUTIONS FOR CATEGORICAL DATA
DISTRIBUTIONS FOR CATEGORICAL DATA 5 present models for a categorcal response wth matched pars; these apply, for nstance, wth a categorcal response measured for the same subjects at two tmes. Chapter 11
More informationEffective September 2015
Annuty rates for all states EXCEPT: NY Lock Polces Prevous Prevous Sheet Feld Bulletns Index Annuty s effectve Monday, September 28 Global Multple Index Cap S&P Annual Pt to Pt Cap MLSB Annual Pt to Pt
More informationSUPPLIER FINANCING AND STOCK MANAGEMENT. A JOINT VIEW.
SUPPLIER FINANCING AND STOCK MANAGEMENT. A JOINT VIEW. Lucía Isabel García Cebrán Departamento de Economía y Dreccón de Empresas Unversdad de Zaragoza Gran Vía, 2 50.005 Zaragoza (Span) Phone: 976-76-10-00
More informationChapter 4 ECONOMIC DISPATCH AND UNIT COMMITMENT
Chapter 4 ECOOMIC DISATCH AD UIT COMMITMET ITRODUCTIO A power system has several power plants. Each power plant has several generatng unts. At any pont of tme, the total load n the system s met by the
More informationCopulas. Modeling dependencies in Financial Risk Management. BMI Master Thesis
Copulas Modelng dependences n Fnancal Rsk Management BMI Master Thess Modelng dependences n fnancal rsk management Modelng dependences n fnancal rsk management 3 Preface Ths paper has been wrtten as part
More informationConstruction Rules for Morningstar Canada Target Dividend Index SM
Constructon Rules for Mornngstar Canada Target Dvdend Index SM Mornngstar Methodology Paper October 2014 Verson 1.2 2014 Mornngstar, Inc. All rghts reserved. The nformaton n ths document s the property
More informationHollinger Canadian Publishing Holdings Co. ( HCPH ) proceeding under the Companies Creditors Arrangement Act ( CCAA )
February 17, 2011 Andrew J. Hatnay ahatnay@kmlaw.ca Dear Sr/Madam: Re: Re: Hollnger Canadan Publshng Holdngs Co. ( HCPH ) proceedng under the Companes Credtors Arrangement Act ( CCAA ) Update on CCAA Proceedngs
More informationCoordinated Denial-of-Service Attacks in IEEE 802.22 Networks
Coordnated Denal-of-Servce Attacks n IEEE 82.22 Networks Y Tan Department of ECE Stevens Insttute of Technology Hoboken, NJ Emal: ytan@stevens.edu Shamk Sengupta Department of Math. & Comp. Sc. John Jay
More informationSection 5.3 Annuities, Future Value, and Sinking Funds
Secton 5.3 Annutes, Future Value, and Snkng Funds Ordnary Annutes A sequence of equal payments made at equal perods of tme s called an annuty. The tme between payments s the payment perod, and the tme
More informationIDENTIFICATION AND CORRECTION OF A COMMON ERROR IN GENERAL ANNUITY CALCULATIONS
IDENTIFICATION AND CORRECTION OF A COMMON ERROR IN GENERAL ANNUITY CALCULATIONS Chrs Deeley* Last revsed: September 22, 200 * Chrs Deeley s a Senor Lecturer n the School of Accountng, Charles Sturt Unversty,
More informationAn Overview of Financial Mathematics
An Overvew of Fnancal Mathematcs Wllam Benedct McCartney July 2012 Abstract Ths document s meant to be a quck ntroducton to nterest theory. It s wrtten specfcally for actuaral students preparng to take
More informationRELIABILITY, RISK AND AVAILABILITY ANLYSIS OF A CONTAINER GANTRY CRANE ABSTRACT
Kolowrock Krzysztof Joanna oszynska MODELLING ENVIRONMENT AND INFRATRUCTURE INFLUENCE ON RELIABILITY AND OPERATION RT&A # () (Vol.) March RELIABILITY RIK AND AVAILABILITY ANLYI OF A CONTAINER GANTRY CRANE
More informationHOUSEHOLDS DEBT BURDEN: AN ANALYSIS BASED ON MICROECONOMIC DATA*
HOUSEHOLDS DEBT BURDEN: AN ANALYSIS BASED ON MICROECONOMIC DATA* Luísa Farnha** 1. INTRODUCTION The rapd growth n Portuguese households ndebtedness n the past few years ncreased the concerns that debt
More information(SOCIAL) COST-BENEFIT ANALYSIS IN A NUTSHELL
(SOCIAL) COST-BENEFIT ANALYSIS IN A NUTSHELL RUFUS POLLOCK EMMANUEL COLLEGE, UNIVERSITY OF CAMBRIDGE 1. Introducton Cost-beneft analyss s a process for evaluatng the merts of a partcular project or course
More informationLinear Circuits Analysis. Superposition, Thevenin /Norton Equivalent circuits
Lnear Crcuts Analyss. Superposton, Theenn /Norton Equalent crcuts So far we hae explored tmendependent (resste) elements that are also lnear. A tmendependent elements s one for whch we can plot an / cure.
More informationA Model of Private Equity Fund Compensation
A Model of Prvate Equty Fund Compensaton Wonho Wlson Cho Andrew Metrck Ayako Yasuda KAIST Yale School of Management Unversty of Calforna at Davs June 26, 2011 Abstract: Ths paper analyzes the economcs
More informationProduct-Form Stationary Distributions for Deficiency Zero Chemical Reaction Networks
Bulletn of Mathematcal Bology (21 DOI 1.17/s11538-1-9517-4 ORIGINAL ARTICLE Product-Form Statonary Dstrbutons for Defcency Zero Chemcal Reacton Networks Davd F. Anderson, Gheorghe Cracun, Thomas G. Kurtz
More informationRegression Models for a Binary Response Using EXCEL and JMP
SEMATECH 997 Statstcal Methods Symposum Austn Regresson Models for a Bnary Response Usng EXCEL and JMP Davd C. Trndade, Ph.D. STAT-TECH Consultng and Tranng n Appled Statstcs San Jose, CA Topcs Practcal
More informationTESTING FOR EVIDENCE OF ADVERSE SELECTION IN DEVELOPING AUTOMOBILE INSURANCE MARKET. Oksana Lyashuk
TESTING FOR EVIDENCE OF ADVERSE SELECTION IN DEVELOPING AUTOMOBILE INSURANCE MARKET by Oksana Lyashuk A thess submtted n partal fulfllment of the requrements for the degree of Master of Arts n Economcs
More informationAllocating Time and Resources in Project Management Under Uncertainty
Proceedngs of the 36th Hawa Internatonal Conference on System Scences - 23 Allocatng Tme and Resources n Project Management Under Uncertanty Mark A. Turnqust School of Cvl and Envronmental Eng. Cornell
More informationCovariate-based pricing of automobile insurance
Insurance Markets and Companes: Analyses and Actuaral Computatons, Volume 1, Issue 2, 2010 José Antono Ordaz (Span), María del Carmen Melgar (Span) Covarate-based prcng of automoble nsurance Abstract Ths
More informationRealistic Image Synthesis
Realstc Image Synthess - Combned Samplng and Path Tracng - Phlpp Slusallek Karol Myszkowsk Vncent Pegoraro Overvew: Today Combned Samplng (Multple Importance Samplng) Renderng and Measurng Equaton Random
More informationKiel Institute for World Economics Duesternbrooker Weg 120 24105 Kiel (Germany) Kiel Working Paper No. 1120
Kel Insttute for World Economcs Duesternbrooker Weg 45 Kel (Germany) Kel Workng Paper No. Path Dependences n enture Captal Markets by Andrea Schertler July The responsblty for the contents of the workng
More informationGlobal Optimization Algorithms with Application to Non-Life Insurance
Global Optmzaton Algorthms wth Applcaton to Non-Lfe Insurance Problems Ralf Kellner Workng Paper Char for Insurance Economcs Fredrch-Alexander-Unversty of Erlangen-Nürnberg Verson: June 202 GLOBAL OPTIMIZATION
More informationNON-CONSTANT SUM RED-AND-BLACK GAMES WITH BET-DEPENDENT WIN PROBABILITY FUNCTION LAURA PONTIGGIA, University of the Sciences in Philadelphia
To appear n Journal o Appled Probablty June 2007 O-COSTAT SUM RED-AD-BLACK GAMES WITH BET-DEPEDET WI PROBABILITY FUCTIO LAURA POTIGGIA, Unversty o the Scences n Phladelpha Abstract In ths paper we nvestgate
More informationENTERPRISE RISK MANAGEMENT IN INSURANCE GROUPS: MEASURING RISK CONCENTRATION AND DEFAULT RISK
ETERPRISE RISK MAAGEMET I ISURACE GROUPS: MEASURIG RISK COCETRATIO AD DEFAULT RISK ADIE GATZERT HATO SCHMEISER STEFA SCHUCKMA WORKIG PAPERS O RISK MAAGEMET AD ISURACE O. 35 EDITED BY HATO SCHMEISER CHAIR
More informationAssurant Employee Benefits City of Frisco Dental DHMO & Dental PPO
Assurant Employee Benefts Cty of Frsco Dental DHMO & Dental PPO Dental Health Goes Beyond Your Teeth Bad dental health mpacts overall health and ncreases the rsk for dabetes, heart dsease, and poor brth
More informationProject Networks With Mixed-Time Constraints
Project Networs Wth Mxed-Tme Constrants L Caccetta and B Wattananon Western Australan Centre of Excellence n Industral Optmsaton (WACEIO) Curtn Unversty of Technology GPO Box U1987 Perth Western Australa
More information1. Math 210 Finite Mathematics
1. ath 210 Fnte athematcs Chapter 5.2 and 5.3 Annutes ortgages Amortzaton Professor Rchard Blecksmth Dept. of athematcal Scences Northern Illnos Unversty ath 210 Webste: http://math.nu.edu/courses/math210
More informationFinite Math Chapter 10: Study Guide and Solution to Problems
Fnte Math Chapter 10: Study Gude and Soluton to Problems Basc Formulas and Concepts 10.1 Interest Basc Concepts Interest A fee a bank pays you for money you depost nto a savngs account. Prncpal P The amount
More informationNordea G10 Alpha Carry Index
Nordea G10 Alpha Carry Index Index Rules v1.1 Verson as of 10/10/2013 1 (6) Page 1 Index Descrpton The G10 Alpha Carry Index, the Index, follows the development of a rule based strategy whch nvests and
More informationTime Value of Money Module
Tme Value of Money Module O BJECTIVES After readng ths Module, you wll be able to: Understand smple nterest and compound nterest. 2 Compute and use the future value of a sngle sum. 3 Compute and use the
More informationAnswer: A). There is a flatter IS curve in the high MPC economy. Original LM LM after increase in M. IS curve for low MPC economy
4.02 Quz Solutons Fall 2004 Multple-Choce Questons (30/00 ponts) Please, crcle the correct answer for each of the followng 0 multple-choce questons. For each queston, only one of the answers s correct.
More informationNONLINEAR OPTIMIZATION FOR PROJECT SCHEDULING AND RESOURCE ALLOCATION UNDER UNCERTAINTY
NONLINEAR OPTIMIZATION FOR PROJECT SCHEDULING AND RESOURCE ALLOCATION UNDER UNCERTAINTY A Dssertaton Presented to the Faculty of the Graduate School of Cornell Unversty In Partal Fulfllment of the Requrements
More informationExhaustive Regression. An Exploration of Regression-Based Data Mining Techniques Using Super Computation
Exhaustve Regresson An Exploraton of Regresson-Based Data Mnng Technques Usng Super Computaton Antony Daves, Ph.D. Assocate Professor of Economcs Duquesne Unversty Pttsburgh, PA 58 Research Fellow The
More informationHow Sets of Coherent Probabilities May Serve as Models for Degrees of Incoherence
1 st Internatonal Symposum on Imprecse Probabltes and Ther Applcatons, Ghent, Belgum, 29 June 2 July 1999 How Sets of Coherent Probabltes May Serve as Models for Degrees of Incoherence Mar J. Schervsh
More informationEffective December 2015
Annuty rates for all states EXCEPT: NY Prevous Index Annuty s effectve Wednesday, December 7 Global Multple Index Cap S&P Annual Pt to Pt Cap MLSB Annual Pt to Pt Spread MLSB 2Yr Pt to Pt Spread 3 (Annualzed)
More information