Moments of the cash value of future payment streams arising from life insurance contracts

A model for the cash value of a stream of future payments arising from an insurance contract, where the interest rate and future-lifetime are random, is studied. A matrix form for formulas for the first two moments of the cash value of the stream of future payments for a portfolio of policies is derived. Numerical illustrations for the rate of interest modeled by a Wiener and an Ornstein–Uhlenbeck process are provided.