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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: J.Spreeuw@city.ac.uk
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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 

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