A general class of risk models

Abstract

We consider the actuarial risk model when the waiting times or claims have a Laplace transform which is a rational function. This generalizes the classical model, where the waiting times are expotenial, and give more flexibility in the modelling of a risk business. Ruin is seen as a random walk crossing a barrier; the summands of the random walk are expressed as the difference of the waiting time and the claim. The class R of distributions which have finite Laplace transforms includes the so-called phase-type distributions. For waiting times in R , the Laplace transform of the ruin probability is obtained explicitly; if the calims are in R , then the probability of ruin is a combination of exponentials times polynomials, which can be found in closed-form.