The Ruin Problem Of A Sparre Andersen Model With The Claim Inter-Occurrence Times Distribution Being Discrete Phase-Type

In this paper,we consider a Sparre Andersen risk model. In this model, the distribution of claim inter-occurrence times is discrete phase-type and the claim size distribution can be discrete. Firstly, the risk process of this model is made into a homogeneous piecewise deterministic Markov process by introducing supplementary components from forward Markoviza-tion technique. Then the martingale approach of piecewise deterministic Markov process(PDMP) and the change of probability measure are used. The general expression, Lundberg bound and Cramer-Lundberg approximation to the ruin probability are derived subsequently. In special case, the explicit expression of the ruin probability is obtained.This paper includes four chapters. In the first chapter, the relative background on this paper is gived. The preparatory knowledge underlying this paper and the model we consider in this paper are introduced in the second one. The third chapter is the main body of this paper, in which the ruin problem of the Sparre Andersen model with discrete phase-type distribution of claim inter-occurrence times is considered. In the last chapter ,the main results of this paper are given.