Modelling Joint Lifetimes of Couples by Using Bivariate Phase-type Distributions

TL;DR

This paper introduces a bivariate phase-type distribution model for joint lifetimes of couples, capturing dependence due to shared factors, with applications in pricing insurance and pension products.

Contribution

It presents a novel Markov process-based model using physiological age to accurately represent joint and last survivor lifetimes with tractable actuarial formulas.

Findings

Model captures dependence between couple lifetimes.

Provides closed-form expressions for actuarial quantities.

Enables pricing of couple-related insurance products.

Abstract

Many insurance products and pension plans provide benefits which are related to couples, and thus under influence of the survival status of two lives. Some studies show the future lifetime of couples is correlated. Three reasons are available to confirm this fact: (1) catastrophe events that affect both lives, (2) the impact of spousal death and (3) the long-term association due to common life style. Dependence between lifetimes of couples could have a financial impact on insurance companies and pension plans providers. In this paper, we use a health index called physiological age in a Markov process context by that we model aging process of joint and last survivor statuses. Under this model, future joint lifetime of couples follows a bivariate phase-type distribution. The model has physical interpretation and closed-form expressions for actuarial quantities and owns tractable computation for the other ones. We use the model to pricing products relevant to couples annuities and life insurances.