Continuity Estimates for Ruin Probabilities

A method of continuity analysis of ruin probabilities with respect to variation of parameters governing risk processes is proposed. It is based on the representation of the ruin probability as the stationary probability of a reversed process. We apply Kartashov's technique designed for continuity analysis of stationary distributions of general Markov chains in order to obtain desired continuity estimates. The method is illustrated by the Sparre Andersen and Markov modulated risk models.