Valuation of Survivorship Life Insurance with Stochastic Rates of Return and Dependent Mortality

Life insurance has been one of the many options for people with concerns about the uncertainty of their future, because it is designed to protect against the serious financial impact that results from an individual's death. An important variation of the single life insurance is the survivorship life insurance which covers two or more lives. Under such contract, a death benefit is paid out only on the last death. Insurance valuation is a very important tool for many insurance companies to be able to know its financial status in order to meet its future obligations. The valuation of an insurance policy comprises of 2 main components, they are: rates of return and mortality assumption. Traditionally, actuaries assume a constant interest rates and an independent mortality assumption in valuing joint-life insurance for the sake of simplicity. However, there has been considerable interest in the actuarial literature in studying the use of stochastic interest rate models and dependent mortality assumptions for insurance valuations. In this study, the mathematical expressions to value survivorship life insurance with stochastic rates of return and dependent mortality are presented. The valuation is conducted by the means of calculation of the expected value of the prospective loss random variable, by assuming an AR(1) process and Frank's Copula to model the rates of return and the dependent mortality of the lifetimes of the policy holders, respectively.