Bankruptcy Of A MAP Risk Model With Perturbations

Since Ncuts(1979) first introduced Markovian arrival risk process (MAP), MAP risk process is one of the important risk processes in risk theory. Because this risk model is closely related to real life. In this process, the evolution of the insurer's surplus is driven by an underlying irreducible continuous-time Markov chain {J(t) : t ? 0} on the state space E = {1. … , m} such that while J(t) = i the Ipremiums are collected linearly at rate ci > 0; claims arriving with a transition from statfe i to state j are assumed to be independent of all other claims, to have distrilbution function Fi,j. The classical risk model, the Phase-type risk model and the Markov modulated risk model are both MAP risk processes. In last thirty years, many authors have considered MAP risk process. Lu and Li (2005) studied the probability of ruin of a Markov-modulated risk model; Li et al. (2015) studied the ruin problems for the MAP risk model. Other papers can be seen Breuer (2002), Badescuet et al. (2005, 2007), Brewer(2008), Ren (2008), Cheung and Landriaclt (2009), Cheung and Feng (2013), Li and Ren (2013), Feng and Shimizu (2014)etc.This paper is organized as follows.In the first, chapter, we introduce the MAP risk process perturbed by diffusion and give some basic knowledge of irreducible continuous-time Markov chain.In chapter 2, the Laplace transform of the ruin time for the MAP risk process per-turbed by diffusion are studied.In the last chapter, we studied the number of claims by the time of ruin for this risk model.