Modeling Broken‐Heart Effect of Insured Couples by Relevation Transform With Proportional Mortality

ABSTRACT

For the remaining lifetimes of an insured couple, dependence arises from not only the shared environment and lifestyle but also the broken‐heart effect well‐documented in demographic and biological studies. However, much of the existing literature lacks an effective way to quantify both sources of dependence. The traditional copula models capture the statistical dependence between spouses but fail to explicitly address the broken‐heart effect, whereas the semi‐Markov chain models incorporate the broken‐heart effect without considering the dependence during marriage. In this paper, we propose a new approach to integrate the broken‐heart effect through the relevation transform and proportional mortality rates. The survival function of lifetimes is derived for an insured couple and its analytical properties are discussed also. This framework enables actuaries to more accurately assess insurance risks associated with couple lifetimes. The advantages of this approach are substantiated through probabilistic analysis, simulation, and empirical study based on a real‐world data application.