Calculation of Ruin Probabilities when the Claim Distribution is Lognormal

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 form where 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.