Hostname: page-component-cd9895bd7-jn8rn Total loading time: 0 Render date: 2024-12-27T13:26:57.787Z Has data issue: false hasContentIssue false
  • English
  • Français

Investigating the Broken-Heart Effect: a Model for Short-Term Dependence between the Remaining Lifetimes of Joint Lives

Published online by Cambridge University Press:  20 November 2012

Jaap Spreeuw  and
Iqbal Owadally
Jaap Spreeuw*
Affiliation:
Cass Business School, City University, London, UK
Iqbal Owadally
Affiliation:
Cass Business School, City University, London, UK
*
*Correspondence to: Jaap Spreeuw, Faculty of Actuarial Science and Insurance, Cass Business School, City University, London EC1Y 8TZ, UK. E-mail: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

We analyze the mortality of couples by fitting a multiple state model to a large insurance data set. We find evidence that mortality rates increase after the death of a partner and, in addition, that this phenomenon diminishes over time. This is popularly known as a “broken-heart” effect and we find that it affects widowers more than widows. Remaining lifetimes of joint lives therefore exhibit short-term dependence. We carry out numerical work involving the pricing and valuation of typical contingent assurance contracts and of a joint life and survivor annuity. If insurers ignore dependence, or mis-specify it as long-term dependence, then significant mis-pricing and inappropriate provisioning can result. Detailed numerical results are presented.

Keywords

Joint livesMultiple life contingenciesBroken-heart syndromeShort-term dependence
Type
Papers
Information
Annals of Actuarial Science , Volume 7 , Issue 2 , September 2013 , pp. 236 - 257
Copyright
Copyright © Institute and Faculty of Actuaries 2012 

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

Andersen, P.K., Borgan, O., Gill, R.D., Keiding, N. (1993). Statistical Models Based on Counting Processes. Springer-Verlag, New York.Google Scholar
Carriere, J.F. (2000). Bivariate survival models for coupled lives. Scandinavian Actuarial Journal, 1(2000), 17–31.Google Scholar
Carriere, J.F., Chan, L.K. (1986). The bounds of bivariate distributions that limit the value of last-survivor annuities. Transactions of the Society of Actuaries, 38, 51–74.Google Scholar
Cox, D.R. (1972). Regression models and life tables (with Discussion). Journal of the Royal Statistical Society, Series B, 34, 187–220.Google Scholar
Denuit, M., Cornet, A. (1999). Multilife premium calculation with dependent future lifetimes. Journal of Actuarial Practice, 7, 147–171.Google Scholar
Denuit, M., Dhaene, J., Le Bailly de Tilleghem, C., Teghem, S. (2001). Measuring the impact of dependence among insured lifelengths. Belgian Actuarial Bulletin, 1, 18–39.Google Scholar
Fleming, T.R., O'Fallon, J.R., O'Brien, P.C., Harrington, D.P. (1980). Modified Kolmogorov-Smirnov test procedures with application to arbitrarily right-censored data. Biometrics, 36(4), 607–625.Google Scholar
Frees, E.W., Carriere, J.F., Valdez, E.A. (1996). Annuity valuation with dependent mortality. Journal of Risk and Insurance, 63(2), 229–261.Google Scholar
Gregorius, F.K. (1993). Disability insurance in the Netherlands. Insurance: Mathematics and Economics, 13, 101–116.Google Scholar
Haberman, S., Pitacco, E. (1999). Actuarial Models for Disability Insurance. Chapman & Hall/CRC, Boca Raton.Google Scholar
Holden, K.C., Kim, J., Novak, B. (2010). Psychological adjustment to widowhood: the role of income, wealth and time. Report to the Pension Section Research Committee, Society of Actuaries, Schaumburg, USA.Google Scholar
Hougaard, P. (2000). Analysis of Multivariate Survival Data. Springer.Google Scholar
Jagger, C., Sutton, C.J. (1991). Death after marital bereavement––is the risk increased? Statistics in Medicine, 10, 395–404.CrossRefGoogle ScholarPubMed
Ji, M. (2011). Markovian approaches to joint life mortality with applications in risk management. PhD Thesis, University of Waterloo, Canada.Google Scholar
Ji, M., Hardy, M.R., Li, J.S.-H. (2011). Markovian approaches to joint life mortality. North American Actuarial Journal, 15(3), 357–376.CrossRefGoogle Scholar
Klein, J.P., Moeschberger, M.L. (1997). Survival Analysis. Techniques for Censored and Truncated Data. Springer-Verlag, New York.Google Scholar
Machin, D., Cheung, Y.B., Parmar, M.K.B. (2006). Survival Analysis. A Practical Approach. Wiley, Chichester, UK.CrossRefGoogle Scholar
Marshall, A.W., Olkin, I. (1967). A multivariate exponential distribution. Journal of the American Statistical Association, 62, 30–44.Google Scholar
Marshall, A.W., Olkin, I. (1988). Families of multivariate distributions. Journal of the American Statistical Association, 88, 834–841.Google Scholar
Möller, C.M. (1990). Select mortality and other durational effects modelled by partially observed Markov chains. Scandinavian Actuarial Journal, 2–3(1990), 177–199.Google Scholar
Norberg, R. (1988). Select mortality: possible explanations. Transactions of the 23rd international Congress of Actuaries, Helsinki, 3, 215–224.Google Scholar
Norberg, R. (1989). Actuarial analysis of dependent lives. Mitteilungen der Schweizerisher Vereinigung der Versicherungsmathematiker 1989, 243–254.Google Scholar
Parkes, C.M., Benjamin, B., Fitzgerald, R.G. (1969). Broken heart: a statistical study of increased mortality among widowers. British Medical Journal, 1(1969), 740–743.Google Scholar
Shemyakin, A., Youn, H. (2006). Copula models of joint last survivor analysis. Applied Stochastic Models in Business and Industry, 22, 211–224.Google Scholar
Spreeuw, J. (2006). Types of dependence and time-dependent association between two lifetimes in single parameter copula models. Scandinavian Actuarial Journal, 5(2006), 286–309.Google Scholar
Wolthuis, H. (2003). Life Insurance Mathematics (The Markovian Model). IAE, Universiteit van Amsterdam, Amsterdam, 2nd edition.Google Scholar
Youn, H., Shemyakin, A. (1999). Statistical aspects of joint life insurance pricing. 1999 Proceedings of the Business and Statistics Section of the American Statistical Association, 34–38.Google Scholar
Youn, H., Shemyakin, A. (2001). Pricing practices for joint last survivor insurance. Actuarial Research Clearing House, 2001.1.Google Scholar