ARCH Proceedings


 Harold Morgan
 3 years ago
 Views:
Transcription
1 Aricle from: ARCH Proceedings Augus 14, 212 Ghislain Leveille, Emmanuel Hamel
2 A renewal model for medical malpracice Ghislain Léveillé École d acuaria Universié Laval, Québec, Canada 47h ARC Conference Winnipeg, Augus 14, 212. * Join work wih Emmanuel Hamel, Universié Laval. 1
3 Absrac A renewal model for he aggregae discouned paymens and expenses assumed by he insurer is proposed for he medical malpracice insurance, where he real ineres raes could be sochasic and he dependency is examined hrough he heory of copulas. As a firs approach o his problem, we presen formulas for he firs wo raw momens and he firs join momen of his aggregae risk process. Examples are given for exponenial claims ineroccurence imes and he dependency is illusraed by an Archimedean copula, in which he auocovariance and he auocorrelaion funcions are also examined. Keywords : Aggregae discouned paymens; Copulas; Join and raw momens; Medical malpracice; Renewal process; Sochasic ineres rae. 2
4 Overview on Medical Malpracice Insurance Definiion : Medical malpracice is generally defined as a professional negligence by ac or omission by a healh care provider in which he reamen provided falls below he acceped sandard of pracice in he medical communiy and evenually causes injury or deah o he paien, wih mos cases involving medical error. Premiums :  Medical malpracice insurers ake several facors ino accoun when seing premiums, and hese are usually charged o individuals, groups of pracice, hospials or governmens. 3
5  One of he main facor is he ype of work a healhcare provider does. Some specialies have a significanly higher rae of claims han ohers and will hus pay higher premiums, such as in neurosurgery and obserics/gynecology.  Anoher imporan facor is he region where a provider pracices. Indeed sandards and regulaions for medical malpracice vary by counry and even by jurisdicions wihin counries, which is paricularly apparen in USA.  Among he oher facors ha are usually considered by he insurer are : some degree of experience raing, adminisraive expenses, liigaion expenses, fuure invesmen income, profi margin sough, insurance business cycle, supply and demand.  The physician professionals claims experience is oo variable over shor ime periods bu presens more sabiliy for hospials. 4
6 Type of insurance :  Premiums will also vary depending on he ype of insurance coverage choosen for medical malpracice.  There are essenially wo primary ypes of insurance coverage for medical malpracice : claimsmade and occurrence policies.  Claimsmade insurance, like auo or home insurance, provides coverage for incidens ha occur while he policy is in force. However, an imporan condiion is ha he claim mus also be filed while he policy is in force for he inciden o be covered. For his ype of insurance, a ail coverage is highly recommended o cover incidens ha have no been repored o he company during he policy erm. 5
7  Occurrence coverage policies differ from he claimsmade coverage by he fac ha hey cover any inciden ha occurs while he policy is in force, no maer when he claim is filed.  As generally observed wihin his insurance marke, he firs ype of insurance is subsanially less expensive in he very firs years bu by he fourh or fifh year i reaches a maure level a abou 95% of he cos of an occurrence policy.  Claimsmade policies are wha are normally issued by mos insurance carriers nowadays. In spie of ha, he decision beween a claimsmade and an occurrence policy will obviously depend of wha is bes suied for he specific needs of he insured eniy. * In his research, only he claimsmade policies will be considered. 6
8 Dependency :  The business line Medical malpracice is characerized by a srong degree of uncerainy under many aspecs ofen relaed.  Many empirical observaions seem o show ha here is a posiive dependency beween he delay from he recepion o he selemen of he claim, he final paymen of he claim and he amoun of expenses allocaed o he claim.  The discoun raes used o acualize he paymen of he claims and he expenses are no necessarily independen.  To represen he dependencies menionned previously, he heory of copulas seems o be mos suiable and has been largely applied in he acuarial lieraure since he las decade. 7
9 A renewal model, wih copula and sochasic ineres rae Moivaed mainly by he works of Léveillé & Garrido (21) and Léveillé & Adékambi (211) on discouned compound renewal sums, we presen a sochasic model for he medical malpracice insurance where he couning process is an ordinary renewal process, he discoun facors relaed o he paymens and he expenses may be sochasic and dependen, and he dependencies are evenually governed by copulas. Hence consider he following aggregae discouned paymens and expenses process Z ( ) = Z 1 ( ) + Z 2 N( ) =: D 1 ( T k + τ k ) X k + D 2 ( T k + τ k )Y k k=1 N( ) k=1 8
10 where { τ k, k } is a sequence of coninuous posiive independen and idenically disribued (i.i.d.) random variables, such ha τ k represens he ineroccurrence ime beween he ( k 1)h and kh claims. { } is a sequence of random variables such ha T k, k T k = k τ k, T =, and hen T k represens he occurrence ime of i=1 he claims received by he insurer. { τ k, k } is a sequence of coninuous posiive i.i.d. random variables, independen of he τ k, such ha τ k is he ime from T k aken by he insurer o pay he kh claim. 9
11 { X k, k } is a sequence of posiive i.i.d. random variables, independen of he T k, such ha X k represens he deflaed amoun of he claim effecively paid by he insurer. { Y k, k } is a sequence of posiive i.i.d. random variables, independen of he T k, such ha Y k represens he deflaed amoun of he expenses incurred by he insurer o fix he paymen corresponding o he kh claim. { } is an ordinary renewal process generaed by he N ( ), ineroccurrence imes { τ k, k }, which represens he number of claims received by he insurer in [,]. 1
12 The random variables X k, Y k and τ k are evenually dependen and his dependency relaion is generaed by a copula C( u 1,u 2,u 3 ), where ( u 1,u 2,u 3 ) [,1] 3, which has posiive measures of dependence and concordance. D i ( ) = exp δ ( u)du, i = 1,2, is he discoun facor a = corresponding o Z i ( ) and δ i ( ) is he force of ne ineres which could be deerminisic or sochasic. Moreover, we will assume ha { δ 1 ( ), } and { δ 2 ( ), } could be dependen bu are independen of he processes { N ( ), }, { τ k, k }, { X k, k } and { Y k, k }. * Here, we make he choice of no represening he possible dependency beween he discoun facors by anoher copula in order no o weigh down our model. 11
13 Firs and second raw momens of Z () The following heorem gives an inegral expression for he firs momen of Z, in agreemen wih our hypoheses. Theorem 1 : Consider he discouned aggregae paymens and expenses process, such as assumed previously. Then, for sochasic forces of ineres δ 1 ( ) and δ 2 ( ), he firs momen of Z is given by : = E X τ = v E D 1 u + v E Z ( ) dm u df τ ( v) + E Y τ = v E D 2 ( u + v) dm( u) df τ ( v), where m( ) is he renewal funcion. 12
14 Corollary 1 : For posiive consan forces of ineres δ 1 and δ 2 Theorem 1 yields E Z = E e δ 1 τ X e δ1v dm v + E e δ 2 τ Y e δ 2v dm v. Example 1: Assume ha he deflaed amouns X k and Y k have respecively, for x >, Pareo disribuions F X ( x) = 1 α1 β 1 β 1 + x, F Y x = 1 α2 β 2 β 2 + x, where β 1 >, β 2 >, α 1 > 2 and α 2 > 2, 13
15 and ha he ineroccurrence imes of he claims τ k and he delays τ k have respecively, for >, exponenial disribuions F τ ( ) = 1 e λ, F τ = 1 e λ, where λ >, λ >. Furhermore assume ha he dependency relaion beween X k, Y k and τ k is generaed by he Archimedian copula = ( 1 u i ) γ C u 1,u 2,u 3 where u 1 = F X 3 i=1 1 γ =:1 f 1 γ ( x), u 2 = F Y ( y), u 3 = F τ ( ) and γ 1. ( u 1,u 2,u 3,γ ), 14
16 Applying Corollary 1, and wih he help of a sofware such as Maple, he preceding ideniy for E Z numerically. [ ] can be calculaed Hence, if we consider he paricular case where δ 1 =.2, δ 2 =.3, α 1 = 3, α 2 = 5, β 1 = β 2 = 1, λ = 1, λ = 2 and γ = 2, hen we ge from Corollary 1 he following funcion for he firs raw momen of Z, E Z ( ) ( 24.48) 1 e.2 + ( 8.1) 1 e.3. * The nex heorem gives an inegral expression for he second momen of Z where he assumed dependencies of he model are also presen in each erm of his expression. 15
17 Theorem 2 : Consider he discouned aggregae paymens and expenses process, such as assumed previously. Then, for sochasic forces of ineres δ 1 ( ) and δ 2 ( ), he second momen of Z is given by: E Z 2 ( ) = E X 2 τ = w + E Y 2 τ = w E D 2 1 E D 2 2 ( v + w) dm v ( v + w) dm v +2 E XY τ = w E D 1 ( v + w)d 2 v + w +2 E X τ = w E X τ = w v E D 1 ( u + w)d 1 u + v + w df τ df τ ( w) ( w) dm v dm( u)dm v df τ df τ ( w) ( w)df τ w 16
18 + 2 E Y τ = w E Y τ = w v E D 2 ( v + w)d 2 u + v + w + 2 E X τ = w E Y τ = w v E D 1 ( v + w)d 2 u + v + w + 2 E X τ = w E Y τ = w v E D 2 ( v + w)d 1 u + v + w dm( u)dm v dm( u)dm v dm( u)dm v df τ df τ df τ ( w)df τ w ( w)df τ w ( w)df τ w 17
19 Corollary 2 : For posiive consan forces of real ineres δ 1 and δ 2, Theorem 2 yields ( ) E Z 2 = E e 2δ 1 τ X 2 e 2δ1v dm v + E e 2δ 2 τ Y 2 e 2δ 2v dm v + 2E e ( δ 1+δ 2 ) τ XY e δ 1+δ 2 v dm v v + 2 E 2 e δ 1 τ X e δ 1( u+2v ) v dm( u)dm( v) + E 2 e δ 2 τ Y e δ 2( u+2v ) dm( u)dm v +E e δ 1 τ X E e δ 2 τ Y e δ 1+δ 2 v v e δ 1u + e δ 2u dm( u)dm v. 18
20 Example 2 : Consider he same disribuions, copula and parameers such as given in Example 1, hen by combining he resuls of Example 1 and Corollary 2 we ge ( ) E Z e e e.5 + 2{ ( 773, 762.5) 1 2e.2 + e , e.3 + e.6 + ( 33, 48.66) 1 e.2 e.3 + e.5 }. 19
21 From Examples 1 and 2, we ge he following able for he expecaion and sandard deviaion of Z ( ), and for a premium based on he sandard deviaion principle. Table 1: E Z, σ Z, Π Z = E Z + σ Z ( ) E Z σ Z Π Z If ime is measured in unis of year and he paid amouns and he expenses are boh measured in unis of $1,, hen we noe ha he premium charged by he insurer is very expensive and increases subsanially wih he insurance coverage period. 2
22 Remark : The choice of he Archimedian copula used in he previous examples is arbirary bu presens posiive measures of concordance and dependence as our model requires i. To verify ha, hereafer we compue (numerically) hree classical measures corresponding o he copula used in our examples, precisely he rivariae Kendall s au τ 3 defined by { } 1 τ 3.354,,1 τ 3 = C ( u 1,u 2,u 3 )dc u 1,u 2,u 3 [ ] 3 he rivariae Spearman s rho ρ 3 defined by, ρ 3 = 8 C( u 1,u 2,u 3 )du 1 du 2 du 3 1 ρ 3.44, [,1] 3 21
23 he mulivariae upper ail dependence coefficien λ U 1..h h+1..3 defined by λ U 1..h h+1..3 = lim u 1 n h i= n n i ( 1 )i ϕ 1 ( iϕ ( u) ) n h n h i ( 1 )i ϕ 1 ( iϕ ( u) ) n i=1, h = 1,2, where ϕ ( u) is he generaor of his Archimedian copula = ln 1 ( 1 u) γ ϕ u ϕ 1 which implies ha 1 λ 2,3 1,2 U.84, λ 3 U.49. ( u) = 1 1 e u γ 1, 22
24 Firs join momen beween Z () and Z (+h) In his secion, we presen an inegral expression for he covariance beween Z ( ) and Z ( + h ), where he erms depending on h are also highly affeced by he dependencies of he model. Theorem 3 : Consider he discouned aggregae paymens and expenses process, such as assumed previously. Then, for sochasic forces of ineres δ 1 ( ) and δ 2 ( ), he firs join momen beween Z and Z ( + h) is given by : E Z ( )Z ( + h) = E Z 2 + E X τ = w E X τ = w +h v E D 1 ( v + w)d 1 u + v + w v dm( u)dm v df τ ( w)df τ w 23
25 + E Y τ = w E Y τ = w +h v E D 2 ( v + w)d 2 u + v + w v + E X τ = w E Y τ = w +h v E D 1 ( v + w)d 2 u + v + w v + E Y τ = w E X τ = w +h v E D 2 ( v + w)d 1 u + v + w v dm( u)dm v dm( u)dm v dm( u)dm v df τ df τ df τ ( w)df τ w ( w)df τ w ( w)df τ w 24
26 Corollary 3 : For posiive consan forces of ineres δ 1 and δ 2, Theorem 3 yields +h v E Z ( )Z ( + h) = E Z 2 ( ) + E 2 e δ 1 τ X e δ 1( u+2v ) dm( u)dm v +E e δ 1 τ X v +h v + E 2 e δ 2 τ Y e δ 2( u+2v ) dm( u)dm v +h v v E e δ 2 τ Y e ( δ 1+δ 2 )v e δ1u + e δ 2u dm( u)dm( v). v 25
27 Example 3 : Again, using he same assumpions and he resuls obained in Examples 1 and 2, we ge E Z ( )Z ( + h) E Z 2 ( ) + 1,498,176 e.2 1 e.2 + ( 72,899.93) e.3 1 e.3 1 e.3h e.2 1 e.2h + 33, e.2h { + e.3 1 e.3h e.5 2 e.2h e.3h }, ( ) where E Z 2 is given in Example 2. 26
28 By using he daa of Table 1, we obain he following able for he auocovariance and auocorrelaion funcions of Z ( ), where we define = C ov Z C,h (, Z ( + h) ), ρ,h = C,h. σ Z ( ) σ Z + h Table 2 : C(,h), ρ(,h). h C 1,h ρ 1,h This able corroboraes he srong linear correlaion observed beween he values of E[ Z ( ) ] in Table 1. Obviously, his las funcion is concave and ends (approximaively) o he value as. 27
29 Conclusion A renewal model for medical malpracice insurance has been proposed. This model incorporaes sochasic ineres raes and a copula o esablish he dependence beween he paymen of he claim, he expenses and he delay beween he receip and he selemen of he claim. Inegral formulas has been given for he firs wo raw momens and he firs join momen of our risk process. The auocorrelaion funcion has also been examined, as well as he incidence of our model on he premium. Several imporan challenges arise now from his model, such as he calibraion of he copulas ha will characerize adequaely he dependency relaions wihin our problem and he choice of he discoun raes ha will bes represen he yields expeced by he insurer, o menion only hose. 28
30 References BHAT, V. N. (21). Medical malpracice: a comprehensive analysis. Auburn House, Connecicu, USA. BORN, P. & BOYER, M. M. (211). ClaimsMade, Repored policies and insurer profiabiliy in medical malpracice, Journal of risk and insurance, 78, 1, De LUCA, G. & RIVIECCIO, G. (212). Mulivariae ail dependence coefficiens for Archimedian copulae, in Advanced Saisical Mehods for he Analysis of Large DaaSes, Springer Sudies in heoreical and applied saisics, FREES, E. W. & VALDEZ, E. A. (1998). Undersanding relaionships using copulas, Norh American Acuarial Journal 2, 1,
31 LÉVEILLÉ, G. & ADÉKAMBI, F. (211) Covariance of discouned compound renewal sums wih a sochasic ineres rae, Scandinavian Acuarial Journal 2, LÉVEILLÉ, G. & GARRIDO, J. (21). Momens of compound renewal sums wih discouned claims. Insurance : Mahemaics and Economics 28 : MELLO, M. M. & PHIL, M. (26). Undersanding medical malpracice insurance: a primer. Research synhesis repor, No. 8. hp:// NELSEN, R. B. (26). An Inroducion o Copulas, 2 nd ed. Springer Series in Saisics. NewYork, USA. 3
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 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 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 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 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 informationMeasuring macroeconomic volatility Applications to export revenue data, 19702005
FONDATION POUR LES ETUDES ET RERS LE DEVELOPPEMENT INTERNATIONAL Measuring macroeconomic volailiy Applicaions o expor revenue daa, 1970005 by Joël Cariolle Policy brief no. 47 March 01 The FERDI is a
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 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 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 informationStochastic 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 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 informationA Reexamination of the Joint Mortality Functions
Norh merican cuarial Journal Volume 6, Number 1, p.166170 (2002) Reeaminaion of he Join Morali Funcions bsrac. Heekung Youn, rkad Shemakin, Edwin Herman Universi of S. Thomas, Sain Paul, MN, US Morali
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 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 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 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 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 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 informationBALANCE OF PAYMENTS. First quarter 2008. Balance of payments
BALANCE OF PAYMENTS DATE: 20080530 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 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 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 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 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 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 informationThe Real Business Cycle paradigm. The RBC model emphasizes supply (technology) disturbances as the main source of
Prof. Harris Dellas Advanced Macroeconomics Winer 2001/01 The Real Business Cycle paradigm The RBC model emphasizes supply (echnology) disurbances as he main source of macroeconomic flucuaions in a world
More informationSPEC 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 informationDOES 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 information4. 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 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 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 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 informationRelationships between Stock Prices and Accounting Information: A Review of the Residual Income and Ohlson Models. Scott Pirie* and Malcolm Smith**
Relaionships beween Sock Prices and Accouning Informaion: A Review of he Residual Income and Ohlson Models Sco Pirie* and Malcolm Smih** * Inernaional Graduae School of Managemen, Universiy of Souh Ausralia
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 informationChapter 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 informationMortality Variance of the Present Value (PV) of Future Annuity Payments
Morali Variance of he Presen Value (PV) of Fuure Annui Pamens Frank Y. Kang, Ph.D. Research Anals a Frank Russell Compan Absrac The variance of he presen value of fuure annui pamens plas an imporan role
More informationCOMPUTATION OF CENTILES AND ZSCORES FOR HEIGHTFORAGE, WEIGHTFORAGE AND BMIFORAGE
COMPUTATION OF CENTILES AND ZSCORES FOR HEIGHTFORAGE, WEIGHTFORAGE AND BMIFORAGE The mehod used o consruc he 2007 WHO references relied on GAMLSS wih he BoxCox power exponenial disribuion (Rigby
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 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 informationForecasting Malaysian Gold Using. GARCH Model
Applied Mahemaical Sciences, Vol. 7, 2013, no. 58, 28792884 HIKARI Ld, www.mhikari.com Forecasing Malaysian Gold Using GARCH Model Pung Yean Ping 1, Nor Hamizah Miswan 2 and Maizah Hura Ahmad 3 Deparmen
More informationMorningstar 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 informationUSE 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 informationDouble 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 informationOn the degrees of irreducible factors of higher order Bernoulli polynomials
ACTA ARITHMETICA LXII.4 (1992 On he degrees of irreducible facors of higher order Bernoulli polynomials by Arnold Adelberg (Grinnell, Ia. 1. Inroducion. In his paper, we generalize he curren resuls on
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 informationBidask Spread and Order Size in the Foreign Exchange Market: An Empirical Investigation
Bidask Spread and Order Size in he Foreign Exchange Marke: An Empirical Invesigaion Liang Ding* Deparmen of Economics, Macaleser College, 1600 Grand Avenue, S. Paul, MN55105, U.S.A. Shor Tile: Bidask
More informationChapter 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 informationAppendix 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\22348900\4
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 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 informationVector Autoregressions (VARs): Operational Perspectives
Vecor Auoregressions (VARs): Operaional Perspecives Primary Source: Sock, James H., and Mark W. Wason, Vecor Auoregressions, Journal of Economic Perspecives, Vol. 15 No. 4 (Fall 2001), 101115. Macroeconomericians
More informationMeasuring the Effects of Exchange Rate Changes on Investment. in Australian Manufacturing Industry
Measuring he Effecs of Exchange Rae Changes on Invesmen in Ausralian Manufacuring Indusry Robyn Swif Economics and Business Saisics Deparmen of Accouning, Finance and Economics Griffih Universiy Nahan
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 informationAnalysis of Tailored BaseSurge Policies in Dual Sourcing Inventory Systems
Analysis of Tailored BaseSurge Policies in Dual Sourcing Invenory Sysems Ganesh Janakiraman, 1 Sridhar Seshadri, 2, Anshul Sheopuri. 3 Absrac We sudy a model of a firm managing is invenory of a single
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 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 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 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 informationII.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 informationThe 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 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 informationPATHWISE 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 informationChapter 9 Bond Prices and Yield
Chaper 9 Bond Prices and Yield Deb Classes: Paymen ype A securiy obligaing issuer o pay ineress and principal o he holder on specified daes, Coupon rae or ineres rae, e.g. 4%, 5 3/4%, ec. Face, par value
More informationNiche 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 informationAs widely accepted performance measures in supply chain management practice, frequencybased service
MANUFACTURING & SERVICE OPERATIONS MANAGEMENT Vol. 6, No., Winer 2004, pp. 53 72 issn 523464 eissn 5265498 04 060 0053 informs doi 0.287/msom.030.0029 2004 INFORMS On Measuring Supplier Performance Under
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 informationHiring as Investment Behavior
Review of Economic Dynamics 3, 486522 Ž 2000. doi:10.1006redy.1999.0084, available online a hp:www.idealibrary.com on Hiring as Invesmen Behavior Eran Yashiv 1 The Eian Berglas School of Economics, Tel
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 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 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 informationPart 1: White Noise and Moving Average Models
Chaper 3: Forecasing From Time Series Models Par 1: Whie Noise and Moving Average Models Saionariy In his chaper, we sudy models for saionary ime series. A ime series is saionary if is underlying saisical
More informationTHE ROLE OF ASYMMETRIC INFORMATION AMONG INVESTORS IN THE FOREIGN EXCHANGE MARKET
INTERNATIONAL JOURNAL OF FINANCE & ECONOMICS In. J. Fin. Econ. (2008) Published online in Wiley InerScience (www.inerscience.wiley.com)..367 THE ROLE OF ASYMMETRIC INFORMATION AMONG INVESTORS IN THE FOREIGN
More informationThe yield curve, and spot and forward interest rates Moorad Choudhry
he yield curve, and spo and forward ineres raes Moorad Choudhry In his primer we consider he zerocoupon or spo ineres rae and he forward rae. We also look a he yield curve. Invesors consider a bond yield
More informationRevisions to Nonfarm Payroll Employment: 1964 to 2011
Revisions o Nonfarm Payroll Employmen: 1964 o 2011 Tom Sark December 2011 Summary Over recen monhs, he Bureau of Labor Saisics (BLS) has revised upward is iniial esimaes of he monhly change in nonfarm
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 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 informationMarkov Chain Modeling of Policy Holder Behavior in Life Insurance and Pension
Markov Chain Modeling of Policy Holder Behavior in Life Insurance and Pension Lars Frederik Brand Henriksen 1, Jeppe Woemann Nielsen 2, Mogens Seffensen 1, and Chrisian Svensson 2 1 Deparmen of Mahemaical
More informationIssues Using OLS with Time Series Data. Time series data NOT randomly sampled in same way as cross sectional each obs not i.i.d
These noes largely concern auocorrelaion Issues Using OLS wih Time Series Daa Recall main poins from Chaper 10: Time series daa NOT randomly sampled in same way as cross secional each obs no i.i.d Why?
More informationInterest Rates and the Market For New Light Vehicles
Federal Reserve Bank of New York Saff Repors Ineres Raes and he Marke For New Ligh Vehicles Adam Copeland George Hall Louis Maccini Saff Repor No. 741 Sepember 2015 This paper presens preliminary findings
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 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 informationModeling Stock Price Dynamics with Fuzzy Opinion Networks
Modeling Sock Price Dynamics wih Fuzzy Opinion Neworks LiXin 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 informationMarket 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 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 informationHedging 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 buyside of a forward/fuures
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 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 informationDefault Risk in Equity Returns
Defaul Risk in Equiy Reurns MRI VSSLOU and YUHNG XING * BSTRCT This is he firs sudy ha uses Meron s (1974) opion pricing model o compue defaul measures for individual firms and assess he effec of defaul
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 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 informationJCER DISCUSSION PAPER No.136
JCER DISCUSSION PAPER No.136 Belief changes and expecaion heerogeneiy in buy and sellside professionals in he Japanese sock marke Ryuichi Yamamoo and Hideaki Hiraa February 2012 公 益 社 団 法 人 日 本 経 済 研
More informationPrice 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 MassachusesAmhers James J. Murphy Deparmen
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 informationDistributing 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 informationTwo Essays on Corporate Income Taxes and Organizational Forms in the United States
Two Essays on Corporae Income Taxes and Organizaional Forms in he Unied Saes A Disseraion Presened o The Academic Faculy By Zhenhua Hu In Parial Fulfillmen Of he Requiremens for he Degree Docor of Philosophy
More informationON THE MULTIPERIOD ECONOMIC RISK CAPITAL OF UNITLINKED LIFE PORTFOLIOS
ON H MULIPRIOD CONOMIC RIK CAPIAL OF UNILINKD LIF PORFOLIO Werner Hürlimann alue and Ris Managemen Winerhur Life and Pensions Posfach 300  CH8401 Winerhur wizerland el. +41522615861  e mail werner.huerlimann@winerhur.ch
More informationProbability Weighting in DamageClaiming Decisions
Probabiliy Weighing in DamageClaiming Decisions Yoram Eden and Doron Sonsino Absrac: We presen experimenal evidence suggesing ha insuranceholders ignore he possibiliy of damagerecurrence when deciding
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 informationI. Basic Concepts (Ch. 14)
(Ch. 14) A. Real vs. Financial Asses (Ch 1.2) Real asses (buildings, machinery, ec.) appear on he asse side of he balance shee. Financial asses (bonds, socks) appear on boh sides of he balance shee. Creaing
More informationSinglemachine Scheduling with Periodic Maintenance and both Preemptive and. Nonpreemptive jobs in Remanufacturing System 1
Absrac number: 050407 Singlemachine Scheduling wih Periodic Mainenance and boh Preempive and Nonpreempive jobs in Remanufacuring Sysem Liu Biyu hen Weida (School of Economics and Managemen Souheas Universiy
More informationBasic Life Insurance Mathematics. Ragnar Norberg
Basic Life Insurance Mahemaics Ragnar Norberg Version: Sepember 22 Conens 1 Inroducion 5 1.1 Banking versus insurance...................... 5 1.2 Moraliy............................... 7 1.3 Banking................................
More information