Calculating Continuous Time Ruin Probabilities for a Large Portfolio with Varying Premiums

In this paper we present a method for the numerical evaluation of the ruin probability in continuous and finite for a classical risk process where the premium can change from year to year. A major consideration in the development of this methodology is that it should be easily applicable to large portfolios. Our method is based on the simulation of the annual aggregate claims and then on the calculation of the ruin probability for a given surplus at the start and at the end of each year. We calculate the within-year ruin probability assuming a translated gamma distribution approximation for aggregate claim amounts. We illustrate our method by studying the case where the premium at the start of each year is a function of the surplus level at that time or at an earlier time.

Keywords: ruin probability, aggregate claims, premiums