Ruin Probabilities In The Compound Random Environment

Risk theory is a very important part in actuarial,which makes use of the methods of probability and stochastic process to establish mathematical about insurance companey's management,and model according to analysis.this thesis is divided to three sections,In Chapter 1,we review the results of ruin theory over the past hundred years.The research of ruin theory begins from Filip Lundberg,on this basis,Harald Cramer and his school set up a relationship between general stochastic process and risk theory.However,as the complexity of the reality background,it is not very appropriate to characterize the risk process of the insurance company with classical risk model,so in recent years,the generalization of the classical risk model has attracted many mathematicians and actuaries,also some good results have been obtained,the risk model has been improved gradually.So in Chapter 2,we give the risk model with a compound Markov binomial model.Recursive formulas are provided for the computation of the ruin probabilities over finite time and infinite time and two examples are also provided. In Chapter 3,we extend this model to n-dimensional Markov chain,some similar conclusions are provided and a Lundberg exponential bond is derived for the ruin probability.