Dynamic Bivariate Mortality Modelling

Abstract

The dependence structure of the life statuses plays an important role in the valuation of life insurance products involving multiple lives. Although the mortality of individuals is well studied in the literature, their dependence remains a challenging field. In this paper, the main objective is to introduce a new approach for analyzing the mortality dependence between two individuals in a couple. It is intended to describe in a dynamic framework the joint mortality of married couples in terms of marginal mortality rates. The proposed framework is general and aims to capture, by adjusting some parametric form, the desired effect such as the "broken-heart syndrome". To this end, we use a well-suited multiplicative decomposition, which will serve as a building block for the framework and thus will be used to separate the dependence structure from the marginals. We make the link with the existing practice of affine mortality models. Finally, given that the framework is general, we propose some illustrative examples and show how the underlying model captures the main stylized facts of bivariate mortality dynamics.