Discrete Time Risk Models under Stochastic Forces of Interest

Discrete time risk models under stochastic forces of interest are discussed. Based on types of payments of premiums, annuity-due and annuity-immediate risk models are introduced. Recursive and integral equations are given for the ruin probabilities in the risk models. Inequalities for the ruin probabilities are derived by martingales and recursive techniques. The inequalities can be used to evaluate the ruin probabilities as upper bounds. Numerical examples are given to illustrate the applications of these results.

Keywords: Discrete time risk model; ruin probability; adjustment coefficient; force of interest; rate of discount; super-martingale; optional stopping theorem; NWU and NBU distribution functions.