On the valuation of life insurance policies for dependent coupled lives

TL;DR

This paper develops a model to price complex life insurance policies for couples with contingent benefits, accounting for interdependent mortality risks and sensitivities to model parameters, providing explicit pricing formulas and insights.

Contribution

It introduces a novel pricing framework for dependent coupled lives with multiple contingent benefits, integrating real-world and risk-neutral measures for comprehensive valuation.

Findings

Explicit pricing expressions derived for complex policies.

Sensitivity analysis highlights impact of joint mortality parameters.

Model captures interdependent risks like broken-heart syndrome.

Abstract

In this paper, we investigate a complex variation of the standard joint life annuity policy by introducing three distinct contingent benefits for the surviving member(s) of a couple, along with a contingent benefit for their beneficiaries if both members pass away. Our objective is to price this innovative insurance policy and analyse its sensitivity to key model parameters, particularly those related to the joint mortality framework. We employ the $QP$-rule (described in Section \ref{secgenset}), which combines the real-world probability measure $P$ for mortality risk with risk-neutral valuation under $Q$ for financial market risks. The model enables explicit pricing expressions, computed using efficient numerical methods. Our results highlight the interdependent risks faced by couples, such as broken-heart syndrome, providing valuable insights for insurers and policyholders regarding the pricing influences of these factors.