Matrix approach to analysis of a portfolio of multistate insurance contracts

This paper discusses the calculation of moments of cash value of future payment streams arising from portfolio of multistate insurance contracts, where the evolution of the insured risk and the interest rate are random. A matrix form for formulas for the first two moments of cash value of the stream of future payments for a portfolio of policies is derived. As an application formulas for insurance premiums are provided. The general theory is illustrated with a case where the rate of interest is modeled by a Wiener and an Ornstein-Uhlenbeck process.