DYNAMIC MODELS FOR VALUATION OF WRONGFUL DEATH PAYMENTS


 Gabriel Preston
 3 years ago
 Views:
Transcription
1 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 winess work, and resoluion in wrongful deah cases, requires esimaion of he amoun of loss. Tha loss resuls from loss of income ha he deceased would have earned had he/she remained alive. The crucial modeling problem is he uncerainy of he fuure income, and he change of i resuling from deah or injury. In his work, we apply he heory of sochasic processes o his problem. We consider he case of a single paymen, and a series of level paymens, corresponding o common mehods of paymens of awards in loss liigaion. We esablish he discouning procedure for he value of fuure salary, and apply sochasic simulaion o deermine loss in case of wrongful deah. We consider discouning wih a single ineres rae, and discouning when ineres raes are modeled wih a sochasic process. We also show ha he models can be exended o injury as well as oher liabiliy cases. INTRODUCTION Liigaion of wrongful deah and injury resuls in an imporan problem of deermining he loss amoun o be compensaed. The loss considered usually refers o income loss of affeced wrongful deah or injury persons minus his (or her) consumpion. Because he income loss of affeced persons is dynamic, ha is o say, he income changes over ime, we mus consider he dynamic change of ineres rae and salary income comprehensively. In his aricle, we deermine he loss compensaed by quaniy analysis and esablishing dynamic model of income loss of wrongful deah. I should be noiced ha i is an imporan work o analyze he changing paern of salary rae wih ime and forecas he income loss ha should be compensaed. There are several aricles ha have sudied his aspec. [2] proposed parameer esimaion of salary funcion, [5] proposed log wage equaion and [3] invesigaed income model of auocorrelaion Y() a + by( 1) + e where Y() is he income, a and b are consans and e is random error a ime. He poined ou ha here exised some limiaion for auo correlaion model, because many economic ime series are nonsaionary. The resuls he analysis relaed change of he series daa of wage raes wih years suppored he assumpion of random walk model. Similar research was discussed by Horviz in [4]. He invesigaed he geomeric Brownian described by he following model Y() Y()e a 1 2 b2 +bz( ), where z() N(,). Anoher imporan issue is how o deermine he discoun value of income excep for forecasing he change paern of wage income wih he ime. In his aricle, we esablish dynamic compensaion models of wrongful deah based on he assuming ha discoun rae is a consan and a sochasic process respecively. We also assume ha he increase rae of wage is a sochasic process and here exiss correlaion beween he discoun rae and he increase rae of wage. The models esablished including he forms of a lumpsum paymen and level paymen. The calculaing mehods can be easily exended o he case of wrongful injury.
2 1. Models of a lump sum paymen Assuming ha he ineres rae is a consan Assume ha a person died in life hur a age. The compensaion paid o his legiimae successor should be equal o he presen value of his cumulaive income from he dae of his deah o he dae of his reiremen ha includes premium for reiremen annuiy minus his consumpion. Here we neglec he addiional paymen for pain and suffering o survivors. We also consider he probabiliy ha he dies in oher acciden or illness. Assume ha he increase rae of wage can be wrien as he following form [6]: dw W µ W d + σ W dz W (1) where µ W is he average wage rae, σ W is he sandard deviaion if wage rae and z W is a sandard Wiener process. Then we have W + µ Ws W s ds + σ Ws W s dz Ws (2) where W is he level of he wage of affeced person when wrongful deah even occurs. When µ W µ W and σ W σ W are consan he sochasic differenial equaion (1) has he unique soluion based on Io s Lemma W e µ W 1 2 σ 2 W +σ W z w (3) Assume ha he random variable T x expresses he survival ime if he affeced person aged x does no die in life hur. Le p x+ Pr ( T x < + 1) express he probabiliy ha a person aged x survives years. The values of p x+ can be found from he life ables. Here we also assume ha T x is a random variable ha is independen of he wage and he ineres rae. Assume ha he age of reiremen is rae is and he risk free ineres, hen he discoun facor calculaed by coninuous ineres rae can be expressed as. To simplify analysis, assume ha he consumpion for a person is h percen of his wage. Le P 1 be he presen value of compensaion of wrongful dearh wih a single paymen, hen P 1 E W (1 h) p x+ E where E denoes he expeced value. Le W (1 h)e(µ W 1 2 σ W 2 )+σ W z w p x+ e r W (1 h)eµ W p x+ e r, (4) e µ W p x+ e r k 1, (5) where k 1 is called as he facor of he compensaion of he wrongful deah wih a single paymen. By
3 combining equaion (5) wih (4), we obain he following equaion: P 1 (1 h)k 1 (6) Assuming ha he ineres rae is a sochasic process As he cumulaive calculaing erm of he compensaion for wrongful dearh is very long, i is very imporan o consider he undeermined characerisic of he ineres rae. I will affec he discoun value of he compensaion. Now we assume ha he real ineres rae can be expressed as he following sochasic differenial equaion: dr β(µ r r)d + σ r dz r (7) (see [1]) where dz r is a sandard Wiener process σ r is he sandard deviaion of ineres rae, µ r is he equilibrium ineres rae of long erm and β is he speed ha he real ineres rae recoveries o he equilibrium ineres rae of long erm. The facor of sochasic discoun calculaing wih coninuous ineres rae can be expressed as e r u du. Assume ha he increase rae of he wage saisfies wih equaion (3), he insan correlaion coefficien beween he wage and he ineres rae is ρ rw and oher assumpions are same as in secion 1. Then he presen value of he compensaion for wrongful deah is E W (1 h) p x+ e r u du}. (8) The paper [7] indicaes ha if he sochasic ineres rae r() follows he sochasic process given by equaion (7), he facor of sochasic discoun is e r u du A()e B( )r, where B() 1 e β β, A() exp (B() ) µ r 1 2 σ r 2 β 2 σ 2 B() r 4β, (9) Therefore, E W (1 h) p x+ A()e By combining equaion (3) wih equaion (1), we obained Le E E B( )r (1) W (1 h)e (µ W 1 2 σ 2 W )+σ W z w B( )r p A()e x+ (11) e (µ W 1 2 σ 2 W )+σ W z w p x B( )r A()e k (12) 2 where k 2 is referred as he facor of compensaion for wrongful deah when he ineres rae is a sochasic process. By combining equaion (12) wih equaion (13), we obain
4 Soluion of (13) is obained wih he help of Mone Carlo simulaion. (1 h)k 2 (13) 2. Models of compensaion for wrongful dearh wih level paymen in n years Because he way of a lump sum paymen needs obligaors o pay a lo of money one ime, someimes, i is difficul o redeem. One effecive mehod o solve his problem is o ake he form of periodical paymen. Assume ha he age he obligaor begins o pay he claim is y, p y+ expresses he probabiliy ha he obligaor aged survives years, and he value of periodical paymen paid a he beginning of each year is AP. Assuming he ineres rae is a consan The sum of presen value ha one dollar is paid a he beginning of each year wihin n years equals 1+ p y+ (14) Based on he principles of acuarial science, he value paid a he beginning of each year by he obligaor should be equal o he value paid a he form of a lump sum divided by he sum of presen value ha one dollar is paid a he beginning of each year wihin n years. Tha is AP 1 E W (1 h)e (µ W 1 2 σ W 1+ p y+ 2 )+σ W z w p x+ e r W (1 h)e µ W p x+ 1+ p y+ (15) Le e µ W p x+ 1+ p y+ k 3 (16) where k 3 is called as he facor of compensaion for he wrongful deah when he ineres rae is a consan. By combining equaion (15) and equaion (16), we obain AP 1 (1 h)k 3 (17) Assuming he ineres rae is a sochasic process The sum of presen value of one dollar paid a he beginning of each year wihin n years equals r u du} 1+ E p y+ e B( )r 1+ E p ( y+ A()e ) (18) Divided by equaion (18), he equaion (11) becomes
5 E A W (1 h)e (µ W 1 2 σ 2 W )+σ W z w B( )r p A()e x+ B( )r ( ) 1+ E p y+ A()e (19) Le E e (µ W 1 2 σ 2 W )+σ W z w B( )r p A()e x+ B( )r ( ) 1+ E p y+ A()e (2) where is called as he facor of compensaion for he wrongful deah when he ineres rae is a sochasic process. By combining equaion (19) wih equaion (2), we obained A (1 h). (21) 3. Calculaion of he compensaion for wrongful deah Assume β.1,σ r.15,σ W.1, µ r.35, µ W.1, ρ rw.2, 5, m 6. When he ineres rae is a consan, r.35. When he ineres rae is a sochasic process, he iniial level of he ineres rae r.3. The probabiliy ha he persons aged and survive years can be found from life ables. Table 1 and Figure 1 liss he values of he facors of he compensaion for he wrongful deah k 1,and calculaed wih he help of Mone Carlo simulaion and equaions of (5), (12), (16) and (2), where he deah age x Leing he iniial wage level when he affeced person dies W muliplied by (1 h) and by he facors of he compensaion for he wrongful deah k 1, and respecively, we can ge he values of he compensaion for he wrongful deah P 1,, AP 1 and A, where he meanings of k 1, and are illusraed in Table 2. Figure 2 is he descripion of he simulaion of sochasic processes when calculaing he facors of he compensaion for wrongful deah. Similarly, we can obain he values of he compensaion for he wrongful deah when he parameers ake oher values.
6 TABLE 1: THE VALUES OF k 1,k 2,k 3,and FOR DIFFERENT x VALUES Source: Auhors calculaion x k k k x k k k TABLE 2: FACTORS OF COMPENSATION FOR WRONGFUL DEATH UNDER DIFFERENT ASSUMPTIONS The ineres rae is a consan The ineres rae is a sochasic process A lump sum paymen Way of paymen Level paymen wihin n years k 1 k 3 k 2 FIGURE 1: THE VALUES OF FOR DIFFERENT VALUES Source: Auhors calculaions
7 FIGURE 2: STOCHASTIC SIMULATION OF THE FACTOR Source: Auhors calculaions Conclusions In his aricle, we apply he sochasic process heory and esablish he sochasic models of he compensaion for he wrongful deah wih a lump sum paymen and level paymen. We also calculae he facors of he compensaion for he wrongful deah k 1, and under various assumpions. Muliplying he facors of he compensaion for he wrongful deah by he difference beween he iniial level of he wage and consumpion of he dead person, we can ge he values of he compensaion for he wrongful deah. The modeling and calculaing process discussed above can be applied o he calculaion of compensaion for he injury case. REFERENCES [1] Babbel, D. F., and C. B. Merrill, IneresSensiive Coningen Claim Valuaion, Sociey of Acuaries, [2] Carriere, J. F. and Shand, K. J., 1998, New Salary Funcions for Pension Valuaions, Norh American Acuarial Journal, Vol. 2, No. 2, pp [3] Hosek, W. R, 1982, Problems in he Use of Hisorical Daa in Esimaing Economic Loss in Wrongful Deah and Injury Cases, Journal of Risk and Insurance, Vol.49, No.2, pp [4] Horviz, S. A, 1986, Implicaions of Projecing Fuure Losses of Earning Capaciy wih Deerminisic Models, Journal of Risk and Insurance, Vol. 53, No. 3, pp [5] Mincer, J. S., 1974, Experience and Earnings, New York: Naional Bureau of Economic Research. [6] Pennacchi, G. G, 1999,The Valuaion of Guaranees on Pension Fund Reurns, Journal of Risk and Insurance, Vol. 66, No. 2, pp [7] Vasicek, O. A., 1977, An Equilibrium Characerizaion of he Term Srucure, Journal of Financial Economics, Vol. 5, pp
Stochastic Optimal Control Problem for Life Insurance
Sochasic Opimal Conrol Problem for Life Insurance s. Basukh 1, D. Nyamsuren 2 1 Deparmen of Economics and Economerics, Insiue of Finance and Economics, Ulaanbaaar, Mongolia 2 School of Mahemaics, Mongolian
More informationOptimal 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 informationLIFE INSURANCE WITH STOCHASTIC INTEREST RATE. L. Noviyanti a, M. Syamsuddin b
LIFE ISURACE WITH STOCHASTIC ITEREST RATE L. oviyani a, M. Syamsuddin b a Deparmen of Saisics, Universias Padjadjaran, Bandung, Indonesia b Deparmen of Mahemaics, Insiu Teknologi Bandung, Indonesia Absrac.
More informationARCH 2013.1 Proceedings
Aricle from: ARCH 213.1 Proceedings Augus 14, 212 Ghislain Leveille, Emmanuel Hamel A renewal model for medical malpracice Ghislain Léveillé École d acuaria Universié Laval, Québec, Canada 47h ARC Conference
More informationModeling VIX Futures and Pricing VIX Options in the Jump Diusion Modeling
Modeling VIX Fuures and Pricing VIX Opions in he Jump Diusion Modeling Faemeh Aramian Maseruppsas i maemaisk saisik Maser hesis in Mahemaical Saisics Maseruppsas 2014:2 Maemaisk saisik April 2014 www.mah.su.se
More informationPROFIT 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 informationDependent Interest and Transition Rates in Life Insurance
Dependen Ineres and ransiion Raes in Life Insurance Krisian Buchard Universiy of Copenhagen and PFA Pension January 28, 2013 Absrac In order o find marke consisen bes esimaes of life insurance liabiliies
More informationOption Pricing Under Stochastic Interest Rates
I.J. Engineering and Manufacuring, 0,3, 889 ublished Online June 0 in MECS (hp://www.mecspress.ne) DOI: 0.585/ijem.0.03. Available online a hp://www.mecspress.ne/ijem Opion ricing Under Sochasic Ineres
More informationJournal 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 YiKang Liu, (yikang@gwu.edu), George Washingon Universiy ABSTRACT The advanage of Mone Carlo
More informationThe Transport Equation
The Transpor Equaion Consider a fluid, flowing wih velociy, V, in a hin sraigh ube whose cross secion will be denoed by A. Suppose he fluid conains a conaminan whose concenraion a posiion a ime will be
More informationTerm 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 111 Nojihigashi, Kusasu, Shiga 5258577, Japan Email:
More informationABSTRACT KEYWORDS. Term structure, duration, uncertain cash flow, variable rates of return JEL codes: C33, E43 1. INTRODUCTION
THE VALUATION AND HEDGING OF VARIABLE RATE SAVINGS ACCOUNTS BY FRANK DE JONG 1 AND JACCO WIELHOUWER ABSTRACT Variable rae savings accouns have wo main feaures. The ineres rae paid on he accoun is variable
More informationA 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 informationWorking 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 informationOptimal Longevity Hedging Strategy for Insurance. Companies Considering Basis Risk. Draft Submission to Longevity 10 Conference
Opimal Longeviy Hedging Sraegy for Insurance Companies Considering Basis Risk Draf Submission o Longeviy 10 Conference Sharon S. Yang Professor, Deparmen of Finance, Naional Cenral Universiy, Taiwan. Email:
More informationMULTIPERIOD OPTIMIZATION MODEL FOR A HOUSEHOLD, AND OPTIMAL INSURANCE DESIGN
Journal of he Operaions Research Sociey of Japan 27, Vol. 5, No. 4, 463487 MULTIPERIOD OPTIMIZATION MODEL FOR A HOUSEHOLD, AND OPTIMAL INSURANCE DESIGN Norio Hibiki Keio Universiy (Received Ocober 17,
More informationA general decomposition formula for derivative prices in stochastic volatility models
A general decomposiion formula for derivaive prices in sochasic volailiy models Elisa Alòs Universia Pompeu Fabra C/ Ramón rias Fargas, 57 85 Barcelona Absrac We see ha he price of an european call opion
More informationOptimal 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 informationThis document is downloaded from DRNTU, Nanyang Technological University Library, Singapore.
This documen is downloaded from DRNTU, Nanyang Technological Universiy Library, Singapore. Tile A Bayesian mulivariae riskneural mehod for pricing reverse morgages Auhor(s) Kogure, Asuyuki; Li, Jackie;
More informationLife insurance cash flows with policyholder behaviour
Life insurance cash flows wih policyholder behaviour Krisian Buchard,,1 & Thomas Møller, Deparmen of Mahemaical Sciences, Universiy of Copenhagen Universiesparken 5, DK2100 Copenhagen Ø, Denmark PFA Pension,
More informationTable 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 informationLEASING 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 informationUNDERSTANDING 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 ErlangenNuremberg Lange Gasse
More informationEstimating TimeVarying Equity Risk Premium The Japanese Stock Market 19802012
Norhfield Asia Research Seminar Hong Kong, November 19, 2013 Esimaing TimeVarying Equiy Risk Premium The Japanese Sock Marke 19802012 Ibboson Associaes Japan Presiden Kasunari Yamaguchi, PhD/CFA/CMA
More informationDuration 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 UVAF38 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 informationECONOMIC AND BUSINESS REVIEW VOL. 13 No. 4 2011 251 272
ECONOMIC AND BUSINESS REVIEW VOL. 13 No. 4 211 251 272 251 ADOPTION OF PROJECTED MORTALITY TABLE FOR THE SLOVENIAN MARKET USING THE POISSON LOGBILINEAR MODEL TO TEST THE MINIMUM STANDARD FOR VALUING LIFE
More informationIndividual Health Insurance April 30, 2008 Pages 167170
Individual Healh Insurance April 30, 2008 Pages 167170 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 informationWhy 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 informationPresent 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 informationValuation of Life Insurance Contracts with Simulated Guaranteed Interest Rate
Valuaion of Life Insurance Conracs wih Simulaed uaraneed Ineres Rae Xia uo and ao Wang Deparmen of Mahemaics Royal Insiue of echnology 100 44 Sockholm Acknowledgmens During he progress of he work on his
More informationPricing Guaranteed Minimum Withdrawal Benefits under Stochastic Interest Rates
Pricing Guaraneed Minimum Wihdrawal Benefis under Sochasic Ineres Raes Jingjiang Peng 1, Kwai Sun Leung 2 and Yue Kuen Kwok 3 Deparmen of Mahemaics, Hong Kong Universiy of Science and echnology, Clear
More informationOptimal Life Insurance Purchase and Consumption/Investment under Uncertain Lifetime
Opimal Life Insurance Purchase and Consumpion/Invesmen under Uncerain Lifeime Sanley R. Pliska a,, a Dep. of Finance, Universiy of Illinois a Chicago, Chicago, IL 667, USA Jinchun Ye b b Dep. of Mahemaics,
More informationDETERMINISTIC INVENTORY MODEL FOR ITEMS WITH TIME VARYING DEMAND, WEIBULL DISTRIBUTION DETERIORATION AND SHORTAGES KUNSHAN WU
Yugoslav Journal of Operaions Research 2 (22), Number, 67 DEERMINISIC INVENORY MODEL FOR IEMS WIH IME VARYING DEMAND, WEIBULL DISRIBUION DEERIORAION AND SHORAGES KUNSHAN WU Deparmen of Bussines Adminisraion
More informationPricing Futures and Futures Options with Basis Risk
Pricing uures and uures Opions wih Basis Risk ChouWen ang Assisan professor in he Deparmen of inancial Managemen Naional Kaohsiung irs niversiy of cience & Technology Taiwan TingYi Wu PhD candidae in
More informationTime Consistency in Portfolio Management
1 Time Consisency in Porfolio Managemen Traian A Pirvu Deparmen of Mahemaics and Saisics McMaser Universiy Torono, June 2010 The alk is based on join work wih Ivar Ekeland Time Consisency in Porfolio Managemen
More informationPricing BlackScholes Options with Correlated Interest. Rate Risk and Credit Risk: An Extension
Pricing Blackcholes Opions wih Correlaed Ineres Rae Risk and Credi Risk: An Exension zulang Liao a, and HsingHua Huang b a irecor and Professor eparmen of inance Naional Universiy of Kaohsiung and Professor
More informationImpact of Debt on Primary Deficit and GSDP Gap in Odisha: Empirical Evidences
S.R. No. 002 10/2015/CEFT Impac of Deb on Primary Defici and GSDP Gap in Odisha: Empirical Evidences 1. Inroducion The excessive pressure of public expendiure over is revenue receip is financed hrough
More informationFifth Quantitative Impact Study of Solvency II (QIS 5) National guidance on valuation of technical provisions for German SLT health insurance
Fifh Quaniaive Impac Sudy of Solvency II (QIS 5) Naional guidance on valuaion of echnical provisions for German SLT healh insurance Conens 1 Inroducion... 2 2 Calculaion of besesimae provisions... 3 2.1
More informationINVESTIGATION OF THE INFLUENCE OF UNEMPLOYMENT ON ECONOMIC INDICATORS
INVESTIGATION OF THE INFLUENCE OF UNEMPLOYMENT ON ECONOMIC INDICATORS Ilona Tregub, Olga Filina, Irina Kondakova Financial Universiy under he Governmen of he Russian Federaion 1. Phillips curve In economics,
More informationBreakeven Determination of Loan Limits for Reverse Mortgages under Information Asymmetry
IRES011016 IRES Working Paper Series Breakeven Deerminaion of Loan Limis for Reverse Morgages under Informaion Asymmery Ming Pu GangZhi Fan Yongheng Deng December, 01 Breakeven Deerminaion of Loan Limis
More information11/6/2013. Chapter 14: Dynamic ADAS. Introduction. Introduction. Keeping track of time. The model s elements
Inroducion Chaper 14: Dynamic DS dynamic model of aggregae and aggregae supply gives us more insigh ino how he economy works in he shor run. I is a simplified version of a DSGE model, used in cuingedge
More informationTEMPORAL 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 informationINVESTMENT GUARANTEES IN UNITLINKED LIFE INSURANCE PRODUCTS: COMPARING COST AND PERFORMANCE
INVESMEN UARANEES IN UNILINKED LIFE INSURANCE PRODUCS: COMPARIN COS AND PERFORMANCE NADINE AZER HAO SCHMEISER WORKIN PAPERS ON RISK MANAEMEN AND INSURANCE NO. 4 EDIED BY HAO SCHMEISER CHAIR FOR RISK MANAEMEN
More informationON THE PRICING OF EQUITYLINKED LIFE INSURANCE CONTRACTS IN GAUSSIAN FINANCIAL ENVIRONMENT
Teor Imov r.amaem.sais. Theor. Probabiliy and Mah. Sais. Vip. 7, 24 No. 7, 25, Pages 15 111 S 949(5)6344 Aricle elecronically published on Augus 12, 25 ON THE PRICING OF EQUITYLINKED LIFE INSURANCE
More information2.5 Life tables, force of mortality and standard life insurance products
Soluions 5 BS4a Acuarial Science Oford MT 212 33 2.5 Life ables, force of moraliy and sandard life insurance producs 1. (i) n m q represens he probabiliy of deah of a life currenly aged beween ages + n
More informationTHE DETERMINATION OF PORT FACILITIES MANAGEMENT FEE WITH GUARANTEED VOLUME USING OPTIONS PRICING MODEL
54 Journal of Marine Science and echnology, Vol. 13, No. 1, pp. 5460 (2005) HE DEERMINAION OF POR FACILIIES MANAGEMEN FEE WIH GUARANEED VOLUME USING OPIONS PRICING MODEL KeeKuo Chen Key words: buildandlease
More informationResearch Article Optimal Geometric Mean Returns of Stocks and Their Options
Inernaional Journal of Sochasic Analysis Volume 2012, Aricle ID 498050, 8 pages doi:10.1155/2012/498050 Research Aricle Opimal Geomeric Mean Reurns of Socks and Their Opions Guoyi Zhang Deparmen of Mahemaics
More informationAnalyzing Surplus Appropriation Schemes in Participating Life Insurance from the Insurer s and the Policyholder s Perspective
Analyzing Surplus Appropriaion Schemes in Paricipaing Life Insurance from he Insurer s and he Policyholder s Perspecive Alexander Bohner, Nadine Gazer Working Paper Chair for Insurance Economics FriedrichAlexanderUniversiy
More informationLongevity 11 Lyon 79 September 2015
Longeviy 11 Lyon 79 Sepember 2015 RISK SHARING IN LIFE INSURANCE AND PENSIONS wihin and across generaions Ragnar Norberg ISFA Universié Lyon 1/London School of Economics Email: ragnar.norberg@univlyon1.fr
More informationTHE 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 informationANALYSIS 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 informationA Brief Introduction to the Consumption Based Asset Pricing Model (CCAPM)
A Brief Inroducion o he Consumpion Based Asse Pricing Model (CCAPM We have seen ha CAPM idenifies he risk of any securiy as he covariance beween he securiy's rae of reurn and he rae of reurn on he marke
More informationPRICING AND PERFORMANCE OF MUTUAL FUNDS: LOOKBACK VERSUS INTEREST RATE GUARANTEES
PRICING AND PERFORMANCE OF MUUAL FUNDS: LOOKBACK VERSUS INERES RAE GUARANEES NADINE GAZER HAO SCHMEISER WORKING PAPERS ON RISK MANAGEMEN AND INSURANCE NO. 4 EDIED BY HAO SCHMEISER CHAIR FOR RISK MANAGEMEN
More informationChapter 6 Interest Rates and Bond Valuation
Chaper 6 Ineres Raes and Bond Valuaion Definiion and Descripion of Bonds Longerm debloosely, bonds wih a mauriy of one year or more Shorerm debless han a year o mauriy, also called unfunded deb Bondsricly
More informationUNIVERSITY OF CALGARY. Modeling of Currency Trading Markets and Pricing Their Derivatives in a Markov. Modulated Environment.
UNIVERSITY OF CALGARY Modeling of Currency Trading Markes and Pricing Their Derivaives in a Markov Modulaed Environmen by Maksym Terychnyi A THESIS SUBMITTED TO THE FACULTY OF GRADUATE STUDIES IN PARTIAL
More informationAn Optimal Strategy of Natural Hedging for. a General Portfolio of Insurance Companies
An Opimal Sraegy of Naural Hedging for a General Porfolio of Insurance Companies HongChih Huang 1 ChouWen Wang 2 DeChuan Hong 3 ABSTRACT Wih he improvemen of medical and hygienic echniques, life insurers
More informationCointegration: The Engle and Granger approach
Coinegraion: The Engle and Granger approach Inroducion Generally one would find mos of he economic variables o be nonsaionary I(1) variables. Hence, any equilibrium heories ha involve hese variables require
More informationMathematics 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 informationAnnuity Decisions with Systematic Longevity Risk
Annuiy Decisions wih Sysemaic Longeviy Risk Ralph Sevens This draf: November, 2009 ABSTRACT In his paper we invesigae he effec of sysemaic longeviy risk, i.e., he risk arising from uncerain fuure survival
More informationINTEREST RATE FUTURES AND THEIR OPTIONS: SOME PRICING APPROACHES
INTEREST RATE FUTURES AND THEIR OPTIONS: SOME PRICING APPROACHES OPENGAMMA QUANTITATIVE RESEARCH Absrac. Exchangeraded ineres rae fuures and heir opions are described. The fuure opions include hose paying
More informationTHE IMPACT OF THE SECONDARY MARKET ON LIFE INSURERS SURRENDER PROFITS
THE IPACT OF THE ECONDARY ARKET ON LIFE INURER URRENDER PROFIT Nadine Gazer, Gudrun Hoermann, Hao chmeiser Insiue of Insurance Economics, Universiy of. Gallen (wizerland), Email: nadine.gazer@unisg.ch,
More informationSecuritization and Tranching Longevity and House Price Risk for Reverse Mortgages
Securiizaion and Tranching Longeviy and House Price Risk for Reverse Morgages Sharon S. Yang 1 Absrac Reverse morgages are new financial producs ha allow he elders o conver heir home equiy ino cash unil
More informationDEMAND FORECASTING MODELS
DEMAND FORECASTING MODELS Conens E2. ELECTRIC BILLED SALES AND CUSTOMER COUNTS Sysemlevel Model Counylevel Model Easside King Counylevel Model E6. ELECTRIC PEAK HOUR LOAD FORECASTING Sysemlevel Forecas
More informationABSTRACT KEYWORDS. Markov chain, Regulation of payments, Linear regulator, Bellman equations, Constraints. 1. INTRODUCTION
QUADRATIC OPTIMIZATION OF LIFE AND PENSION INSURANCE PAYMENTS BY MOGENS STEFFENSEN ABSTRACT Quadraic opimizaion is he classical approach o opimal conrol of pension funds. Usually he paymen sream is approximaed
More informationCLASSIFICATION OF REINSURANCE IN LIFE INSURANCE
CLASSIFICATION OF REINSURANCE IN LIFE INSURANCE Kaarína Sakálová 1. Classificaions of reinsurance There are many differen ways in which reinsurance may be classified or disinguished. We will discuss briefly
More informationOptimal Life Insurance Purchase, Consumption and Investment
Opimal Life Insurance Purchase, Consumpion and Invesmen Jinchun Ye a, Sanley R. Pliska b, a Dep. of Mahemaics, Saisics and Compuer Science, Universiy of Illinois a Chicago, Chicago, IL 667, USA b Dep.
More informationA Universal Pricing Framework for Guaranteed Minimum Benefits in Variable Annuities *
A Universal Pricing Framework for Guaraneed Minimum Benefis in Variable Annuiies * Daniel Bauer Deparmen of Risk Managemen and Insurance, Georgia Sae Universiy 35 Broad Sree, Alana, GA 333, USA Phone:
More informationA Generalized Bivariate OrnsteinUhlenbeck Model for Financial Assets
A Generalized Bivariae OrnseinUhlenbeck Model for Financial Asses Romy Krämer, Mahias Richer Technische Universiä Chemniz, Fakulä für Mahemaik, 917 Chemniz, Germany Absrac In his paper, we sudy mahemaical
More informationA TwoAccount Life Insurance Model for ScenarioBased Valuation Including Event Risk Jensen, Ninna Reitzel; Schomacker, Kristian Juul
universiy of copenhagen Universiy of Copenhagen A TwoAccoun Life Insurance Model for ScenarioBased Valuaion Including Even Risk Jensen, Ninna Reizel; Schomacker, Krisian Juul Published in: Risks DOI:
More informationChapter 7. Response of FirstOrder RL and RC Circuits
Chaper 7. esponse of FirsOrder 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 informationYTM is positively related to default risk. YTM is positively related to liquidity risk. YTM is negatively related to special tax treatment.
. Two quesions for oday. A. Why do bonds wih he same ime o mauriy have differen YTM s? B. Why do bonds wih differen imes o mauriy have differen YTM s? 2. To answer he firs quesion les look a he risk srucure
More informationDynamic Option Adjusted Spread and the Value of Mortgage Backed Securities
Dynamic Opion Adjused Spread and he Value of Morgage Backed Securiies Mario Cerrao, Abdelmadjid Djennad Universiy of Glasgow Deparmen of Economics 27 January 2008 Absrac We exend a reduced form model for
More informationIndexing Executive Stock Options Relatively
Indexing Execuive Sock Opions Relaively JinChuan Duan and Jason Wei Joseph L. Roman School of Managemen Universiy of Torono 105 S. George Sree Torono, Onario Canada, M5S 3E6 jcduan@roman.uorono.ca wei@roman.uorono.ca
More informationThis page intentionally left blank
This page inenionally lef blank MarkeValuaion Mehods in Life and Pension Insurance In classical life insurance mahemaics, he obligaions of he insurance company owards he policy holders were calculaed
More informationHouse Price Index (HPI)
House Price Index (HPI) The price index of second hand houses in Colombia (HPI), regisers annually and quarerly he evoluion of prices of his ype of dwelling. The calculaion is based on he repeaed sales
More informationRationales 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 informationA General Pricing Framework for NoNegativeEquity. Guarantees with Equityrelease Products: A Theoretical and
A General Pricing Framework for NoNegaiveEquiy Guaranees wih Equiyrelease Producs: A Theoreical and Empirical Sudy JrWei Huang 1 ChuangChang Chang 2 Sharon S. Yang 3 ABSTRACT We invesigae sochasic
More informationOptimal Investment, Consumption and Life Insurance under MeanReverting Returns: The Complete Market Solution
Opimal Invesmen, Consumpion and Life Insurance under MeanRevering Reurns: The Complee Marke Soluion Traian A. Pirvu Dep of Mahemaics & Saisics McMaser Universiy 180 Main Sree Wes Hamilon, ON, L8S 4K1
More informationIMPLICIT OPTIONS IN LIFE INSURANCE CONTRACTS FROM OPTION PRICING TO THE PRICE OF THE OPTION. Tobias Dillmann * and Jochen Ruß **
IMPLICIT OPTIONS IN LIFE INSURANCE CONTRACTS FROM OPTION PRICING TO THE PRICE OF THE OPTION Tobias Dillmann * and Jochen Ruß ** ABSTRACT Insurance conracs ofen include socalled implici or embedded opions.
More informationThe Relationship between Stock Return Volatility and. Trading Volume: The case of The Philippines*
The Relaionship beween Sock Reurn Volailiy and Trading Volume: The case of The Philippines* Manabu Asai Faculy of Economics Soka Universiy Angelo Unie Economics Deparmen De La Salle Universiy Manila May
More informationMTH6121 Introduction to Mathematical Finance Lesson 5
26 MTH6121 Inroducion o Mahemaical Finance Lesson 5 Conens 2.3 Brownian moion wih drif........................... 27 2.4 Geomeric Brownian moion........................... 28 2.5 Convergence of random
More informationChapter 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 informationRisk Modelling of Collateralised Lending
Risk Modelling of Collaeralised Lending Dae: 4112008 Number: 8/18 Inroducion This noe explains how i is possible o handle collaeralised lending wihin Risk Conroller. The approach draws on he faciliies
More informationThe 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 informationRandom Walk in 1D. 3 possible paths x vs n. 5 For our random walk, we assume the probabilities p,q do not depend on time (n)  stationary
Random Walk in D Random walks appear in many cones: diffusion is a random walk process undersanding buffering, waiing imes, queuing more generally he heory of sochasic processes gambling choosing he bes
More informationA Note on Construction of Multiple Swap Curves with and without Collateral
A Noe on Consrucion of Muliple Swap Curves wih and wihou Collaeral Masaaki Fujii, Yasufumi Shimada, Akihiko Takahashi Absrac There are now available wide variey
More informationStochastic Volatility Models: Considerations for the Lay Actuary 1. Abstract
Sochasic Volailiy Models: Consideraions for he Lay Acuary 1 Phil Jouber Coomaren Vencaasawmy (Presened o he Finance & Invesmen Conference, 191 June 005) Absrac Sochasic models for asse prices processes
More informationReturn Calculation of U.S. Treasury Constant Maturity Indices
Reurn Calculaion of US Treasur Consan Mauri Indices Morningsar Mehodolog Paper Sepeber 30 008 008 Morningsar Inc All righs reserved The inforaion in his docuen is he proper of Morningsar Inc Reproducion
More information= r t dt + σ S,t db S t (19.1) with interest rates given by a mean reverting OrnsteinUhlenbeck or Vasicek process,
Chaper 19 The BlackScholesVasicek Model The BlackScholesVasicek model is given by a sandard imedependen BlackScholes model for he sock price process S, wih imedependen bu deerminisic volailiy σ
More informationChapter 8 Student Lecture Notes 81
Chaper Suden Lecure Noes  Chaper Goals QM: Business Saisics Chaper Analyzing and Forecasing Series Daa Afer compleing his chaper, you should be able o: Idenify he componens presen in a ime series Develop
More informationMarket Analysis and Models of Investment. Product Development and Whole Life Cycle Costing
The Universiy of Liverpool School of Archiecure and Building Engineering WINDS PROJECT COURSE SYNTHESIS SECTION 3 UNIT 11 Marke Analysis and Models of Invesmen. Produc Developmen and Whole Life Cycle Cosing
More informationDeveloping Equity Release Markets: Risk Analysis for Reverse Mortgage and Home Reversion
Developing Equiy Release Markes: Risk Analysis for Reverse Morgage and Home Reversion Daniel Alai, Hua Chen, Daniel Cho, Kaja Hanewald, Michael Sherris Developing he Equiy Release Markes 8 h Inernaional
More informationCarbon Trading. Diederik Dian Schalk Nel. Christ Church University of Oxford
Carbon Trading Diederik Dian Schalk Nel Chris Church Universiy of Oxford A hesis submied in parial fulfillmen for he MSc in Mahemaical inance April 13, 29 This hesis is dedicaed o my parens Nana and Schalk
More informationDemand and Price Forecasting Models for Strategic and Planning Decisions in a Supply Chain
Proc. Schl. ITE Tokai Univ. vol.3,no,,pp.374 Vol.,No.,,pp.  Paper Demand and Price Forecasing Models for Sraegic and Planning Decisions in a Supply Chain by Vichuda WATTANARAT *, Phounsakda PHIMPHAVONG
More informationSkewness and Kurtosis Adjusted BlackScholes Model: A Note on Hedging Performance
Finance Leers, 003, (5), 6 Skewness and Kurosis Adjused BlackScholes Model: A Noe on Hedging Performance Sami Vähämaa * Universiy of Vaasa, Finland Absrac his aricle invesigaes he dela hedging performance
More informationStochastic Calculus and Option Pricing
Sochasic Calculus and Opion Pricing Leonid Kogan MIT, Sloan 15.450, Fall 2010 c Leonid Kogan ( MIT, Sloan ) Sochasic Calculus 15.450, Fall 2010 1 / 74 Ouline 1 Sochasic Inegral 2 Iô s Lemma 3 BlackScholes
More informationIf You Are No Longer Able to Work
If You Are No Longer Able o Work NY STRS A Guide for Making Disabiliy Reiremen Decisions INTRODUCTION If you re forced o sop working because of a serious illness or injury, you and your family will be
More informationRisk management and regulatory aspects of life insurance companies with a special focus on disability insurance
Risk managemen and regulaory aspecs of life insurance companies wih a special focus on disabiliy insurance Disseraion zur Erlangung des akademischen Grades eines Dokors der Wirschafswissenschafen (Dr.
More informationOption PutCall Parity Relations When the Underlying Security Pays Dividends
Inernaional Journal of Business and conomics, 26, Vol. 5, No. 3, 22523 Opion Puall Pariy Relaions When he Underlying Securiy Pays Dividends Weiyu Guo Deparmen of Finance, Universiy of Nebraska Omaha,
More informationPricing FixedIncome Derivaives wih he ForwardRisk Adjused Measure Jesper Lund Deparmen of Finance he Aarhus School of Business DK8 Aarhus V, Denmark Email: jel@hha.dk Homepage: www.hha.dk/~jel/ Firs
More information