Survey For Ruin Probability With Phase-Type Claim Amounts

Ruin probability is an interesting topic in actuarial mathematics. Phase-type distribution is an extremely popular tool for applied probability wishing to generalize beyond the exponential while retaining some of its key properties. In this paper we study the ruin probability in classical risk model with phase type claim amounts. First the clear descriptions about basic assumptions of classical risk model is given. We introduce the phase type distribution according to the probability of the Markov process into an absorbing state. Next an explicit formula of ruin probability are presented in classical risk model when the individual claim amount is phase type distribution. Finally, we present three numerical examples at the end of paper for illustration. With the help of Matlab, we give exactly results of ultimate ruin probability.