Cramer-Lundberg model for some classes of extremal Markov sequences

Abstract

We consider here the Cramer-Lundberg model based on generalized convolutions. In our model the insurance company invests at least part of its money, have employees, shareholders. The financial situation of the company after paying claims can be even better than before. We compute the ruin probability for α-convolution case, maximal convolution and the Kendall convolution case, which is formulated in the Williamson transform terms. We also give some new results on the Kendall random walks.