Calculation of Ruin Probabilities when the Claim Distribution is Lognormal

Abstract

In this paper some ruin probabilities are calculated for an example of a lognormal claim distribution. For that purpose it is shown that the lognormal distribution function, Λ(y), may be written in the formwhere V(x) is absolutely continuous and without being a distribution function preserves some useful properties of such a function.An attempt is also made to give an approximant Λα(y) to Λ(y) such that Λα(y) is a linear combination of a low number of exponential distributions. For comparison, ruin probabilities are also calculated for two examples of Λα(y).In the considered numerical cases it is assumed that the occurrence of claims follows a Poisson process.