Analysis of Joint Life Insurance with Stochastic Interest Rates

A general portfolio of joint life insurance contracts is studied in a stochastic interest rate environment with independent and dependent mortality models. Two types of joint insurance products, namely joint first-to-die and joint last-to-die, are considered in this project. Two methods are used to derive the first two moments of the prospective loss random variable. The first one is based on the individual loss random variables while the second one studies annual stochastic cash flows. The total riskiness of the portfolio is decomposed into its insurance risk and its investment risk. For illustrative purposes, an AR(1) process is used to model the stochastic interest rates. Copula and common shock models are used to model dependence in mortality. The effects of mortality dependence on the riskiness of portfolios of joint life insurances are analyzed.