On bivariate lifetime modelling in life insurance applications

TL;DR

This paper models the dependence between lifetimes in married couples using copulas, revealing how age difference and gender influence correlation, with practical implications for life insurance products.

Contribution

It introduces a novel copula-based model incorporating age difference and gender as dependence parameters, validated with real Canadian insurance data.

Findings

Dependence decreases with age difference

Higher dependence when husband is older

Model fits well with real data

Abstract

Insurance and annuity products covering several lives require the modelling of the joint distribution of future lifetimes. In the interest of simplifying calculations, it is common in practice to assume that the future lifetimes among a group of people are independent. However, extensive research over the past decades suggests otherwise. In this paper, a copula approach is used to model the dependence between lifetimes within a married couple \eH{using data from a large Canadian insurance company}. As a novelty, the age difference and the \eH{gender} of the elder partner are introduced as an argument of the dependence parameter. \green{Maximum likelihood techniques are} thus implemented for the parameter estimation. Not only do the results make clear that the correlation decreases with age difference, but also the dependence between the lifetimes is higher when husband is older than wife. A goodness-of-fit procedure is applied in order to assess the validity of the model. Finally, considering several products available on the life insurance market, the paper concludes with practical illustrations.