THE NON-RUIN PROBABILITY FOR THE RISK RESERVE PROCESS WITH ERLANG TYPE CLAIMS

Abstract

In this paper, we consider the risk reserve process with Erlang type claims. We make the model that the claim inter-arrival time has an exponential distribution and the claim size has an Erlang distribution. For this model we obtain a general formula that derives the non-ruin probability in finite time. In order to have an easy calculation for the non-ruin probability we reduce the multi-summation to the singlesummation.