On ruin probabilities in risk models with interest rate

Abstract

An explicit formula for the finite-time ruin probability in a discrete-time collective ruin model with constant interest rate is found under the assumption that claims follow a generalised hyperexponential distribution. The formula can be used for finding approximations for finite-time ruin probabilities in the case when claim sizes follow a heavy-tailed distribution e.g. Pareto. We also provide theoretical bounds for the accuracy of approximations of the finite-time ruin probabilities in terms of a distance between the distribution of claims and its approximation. Results of numerical comparisons with asymptotic formulas and simulations are presented.9 page(s