The premium and the risk of a life policy in the presence of interest rate fluctuations

In this work, we consider the premium setting and the associated risk with regard to a life insurance policy when the interest rate process is a diffusion. Explicit formulas and numerical examples are given for the premiums determined by the equivalence principle under some well-known interest rate models such as the Vasicek model and the CIR model. Two types of premium design, single deposit premium and continuous premium, are considered. A martingale related to the discounted reserve process is introduced. With this martingale, an analysis of the risk of ruin is also carried out on a collective basis when the premium is the natural premium plus an initial positive loading. A bound of exponential type is derived for the ruin probability.