A Class Of Risk Model With Claim Inter-Arrival Times Distributed As Erlang

This paper includes three chapters. Two chapters of beginning are the preparatory knowledge and the introduction of achievement which come from [6] and [12]. The main part of this paper is chapter 3 where we consider a class of risk model with claim inter-arrival times distributed as Erlang.Piecewise deterministic Markov processes(PDMP) have important application in risk theory, especially the theory of martingal on the basis of PDMP has offered the method to stylize for studying risk theory. In this paper we consider a class of risk model with claim inter-arrival times distributed as Erlang by the means of PDMP and the change of measure. We include the risk model in the frame of PDMP and get martingal by solving the equation Ag = 0, then we can get the Lundberg's inequality of the ruin probability, C-L approximation, finite-horizon ruin probability and so on. Especially, we can get the exact solution in the case where the individual claim amount distribution is exponential.