Hostname: page-component-76fb5796d-25wd4 Total loading time: 0 Render date: 2024-04-26T02:31:35.467Z Has data issue: false hasContentIssue false
  • English
  • Français

JOINT LIFE INSURANCE PRICING USING EXTENDED MARSHALL–OLKIN MODELS

Published online by Cambridge University Press:  01 March 2019

Fabio Gobbi ,
Nikolai Kolev  and
Sabrina Mulinacci
Fabio Gobbi
Affiliation:
Department of Statistics, University of Bologna,Italy E-mail: fabio.gobbi@unibo.it
Nikolai Kolev
Affiliation:
Institute of Mathematics and Statistics, University of São Paulo, Brazil E-mail: kolev.ime@gmail.com
Sabrina Mulinacci*
Affiliation:
Department of Statistics, University of Bologna, Italy E-mail: sabrina.mulinacci@unibo.it
*
E-mail: sabrina.mulinacci@unibo.it
Get access Rights & Permissions [Opens in a new window]

Abstract

In this paper we suggest a modeling of joint life insurance pricing via Extended Marshall–Olkin (EMO) models and related copulas. These models are based on the combination of two approaches: the absolutely continuous copula approach, where the copula is used to capture dependencies due to environmental factors shared by the two lives, and the classical Marshall–Olkin model, where the association is given by accounting for a fatal event causing the simultaneous death of the two lives. New properties of the EMO model are established and applied to a sample of censored residual lifetimes of couples of insureds extracted from a data set of annuities contracts of a large Canadian life insurance company. Finally, some joint life insurance products are analyzed.

Keywords

Bivariate Marshall–Olkin’s modelcopulamortality intensitysingularityjoint life insurance products
Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 49 , Issue 2 , May 2019 , pp. 409 - 432
Copyright
Copyright © Astin Bulletin 2019 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Asimit, V., Furman, E. and Vernic, R. (2016) Statistical inference for a new class of multivariate pareto distributions. Communications in Statistics - Simulation and Computation, 45(2), 456–471.CrossRefGoogle Scholar
Bowers, N.L., Gerber, U., Hickman, J.C., Jones, D.A. and Nesbit, C.J. (1997) Actuarial Mathematics. School of Actuaries.Google Scholar
Carriere, J. (2000) Bivariate survival models of coupled lives. Scandinavian Actuarial Journal, 2000(1), 17–31.CrossRefGoogle Scholar
Denuit, M., Dhaene, J., Le Bailly De Tilleghem, C. and Teghem, S. (2001) Measuring the impact of dependence among insured lifelengths. Belgian Actuarial Bulletin, 1, 18–39.Google Scholar
Denuit, M., Frostig, E. and Levikson, B. (2006) Shift in interest rate and common shock model for coupled lives. Belgian Actuarial Bulletin, 6, 1–4.Google Scholar
Dufresne, F.Hashrova, E., Ratovomirija, G. and Toukourou, Y. (2018) On age difference in joint lifetime modelling with life insurance annuity applications. Annals of Actuarial Sciences, 12(2), 350–371.CrossRefGoogle Scholar
Frees, E., Carriere, J. and Valdez, E. (1996) Annuity valuation with dependent mortality. Journal of Risk and Insurance, 63, 229–261.CrossRefGoogle Scholar
Gouriéroux, C. and Lu, Y. (2015) Love and death: A Freund model with frailty. Insurance: Mathematics and Economics, 63, 191–203.Google Scholar
Ji, M., Hardy, M.R. and Li, J.S.-H. (2011) Markovian approaches to joint-life mortality. North American Actuarial Journal, 15(3), 357–376.CrossRefGoogle Scholar
Karlis, D. (2003) ML estimation for multivariate shock models via an EM algorithm. Annals of the Institute of Statistical Mathematics, 155, 817–830.CrossRefGoogle Scholar
Kolev, N. and Pinto, J. (2018) A weak version of bivariate lack of memory property. Brazilian Journal of Probability and Statistics, 32(4), 873–906.CrossRefGoogle Scholar
Kundu, D. and Dey, A. (2009) Estimating the parameters of the Marshall Olkin bivariate Weibull distribution. Computational Statistics and Data Analysis, 57, 271–281.CrossRefGoogle Scholar
Kundu, D. and Gupta, A. (2013) Bayes estimation for the Marshall-Olkin bivariate Weibull distribution by EM algorithm. Computational Statistics and Data Analysis, 53, 956–965.CrossRefGoogle Scholar
Lee, H. and Cha, J.H. (2018) A dynamic bivariate common shock model with cumulative effect and its actuarial application. Scandinavian Actuarial Journal. DOI:10.1080/03461238.2018.1470562.CrossRefGoogle Scholar
Li, X. and Pellerey, F. (2011) Generalized Marshall-Olkin distribution and related bivariate aging properties. Journal of Multivariate Analysis, 102(10), 1399–1409.CrossRefGoogle Scholar
Lu, Y. (2017) Broken-Heart, common life, heterogeneity: Analyzing the spousal mortality dependence. ASTIN Bulletin: the Journal of the IAA, 47(3), 837–874.CrossRefGoogle Scholar
Luciano, E., Spreeuw, J. and Vigna, E. (2008) Modelling stochastic mortality for dependent lives. Insurance: Mathematics and Economics, 43, 234–244.Google Scholar
Luciano, E., Spreeuw, J. and Vigna, E. (2016) Spouses’ dependence across generations and pricing impact on reversionary annuities. Risks, 4(2), 1–18.CrossRefGoogle Scholar
Marshall, A.W. and Olkin, I. (1967) A multivariate exponential distribution. Journal of the American Statistical Association, 62, 30–44.CrossRefGoogle Scholar
Nelsen, R. (2006) An Introduction to Copulas. New York: Springer.Google Scholar
Oakes, D. (1989) Bivariate survival models induced by frailties. Journal of the American Statistical Association, 84(406), 487–493.CrossRefGoogle Scholar
Pinto, J. and Kolev, N. (2015) Extended Marshall-Olkin Model and its dual version. In Marshall-Olkin Distributions-Advances in Theory and Applications. Springer Proceedings in Mathematics and Statistics (eds. Cherubini, U., Durante, F. and Mulinacci, S.), pp. 87–113. Springer International Publishing Switzerland.CrossRefGoogle Scholar
Shemyakin, A. and Youn, H. (2006) Copula models of joint last survivor analysis. Applied Stochastic Models in Business and Industry, 22, 211–224.CrossRefGoogle Scholar
Shih, J.H. and Louis, T.A. (1995) Inferences on the association parameter in copula models for bivariate survival data. Biometrics, 51, 1384–1399.CrossRefGoogle ScholarPubMed
Sibuya, M. (1960) Bivariate extreme statistics. Annals of the Institute of Statistical Mathematics, 11, 195–210.CrossRefGoogle Scholar
Spreeuw, J. (2006) Types of dependence and time-dependent association between two lifetimes in single parameter copula models. Scandinavian Actuarial Journal, 5, 286–309.CrossRefGoogle Scholar
Spreeuw, J. and Wang, X. (2008) Modelling the short-term dependence between two remaining lifetimes, Cass Business School Discussion Paper.Google Scholar
Spreeuw, J. and Owadally, I. (2013) Investigating the broken-heart effect: A model for short-term dependence between the remaining lifetimes of joint lives. Annals of Actuarial Science, 7(2), 236–257.CrossRefGoogle Scholar
Volinsky, C.T. and Raftery, A.E. (2000) Bayesian information criterion for censored survival models. Biometrics, 56, 256–262.CrossRefGoogle ScholarPubMed
Youn, H. and Shemyakin, A. (1999) Statistical aspects of joint life insurance pricing. In Proceedings of the Business and Statistics Section of the American Statistical Association, pp. 34–38.Google Scholar