The moments of ruin time in the classical risk model with discrete claim size distribution
The authors consider a classical ruin model with discrete claim sizes \(W_i\), constant claim intensity \(c\) and constant premium rate \(\lambda\). Exact simple solutions are provided for the moments \(k\) of ruin time for the case where the initial reserve \(u=0\). Also, for the case of \(u\) natural, an analytic expression is derived. The calculation involves recursive calculations in terms of \(k\) and \(u\) which can be rolled out into finite sums over \(r,\dots,u\). The calculations are built on a generalized Appell structure of polynomials. Both cases \(c>\) and \(c\leq\lambda E[W_i]\) are treated.
scientific article; zbMATH DE number 1251567