Study Of Several Amounts Of Risk In The Markovian Risk Model

Classical risk model is a basic mathematic model of describing the surplus process of an insurance company, by which we studied the ruin probabilities with a "small claim". With the more and more occurrences of some large claim businesses, a new risk model was needed to meet the real cases. Thus, the risk model described by a Markov jump process came into being. In this model, we assume that there exists a Markov jump process with a finite state space, and the occurrence process of claims is described by a point process of{N(t)}t>o with N(t) being the number of jumps of the Markov jump process during the interval (0,t]. In this paper, we mainly study several types of risk problems in the Markovian risk model.In the first chapter, a brief introduction of the research background and the status of the risk model is given. Then we also present the problems solved in this paper.In the second chapter, we introduce the basic theory related to this paper, including the classical risk model, the Markov jump process and the Markovian risk model.In the third chapter, we mainly study survival probabilities under the Marko-vian risk model. Then supposing the claims with the Erlang(2), Erlang(n) and mixed-Erlang(2) distribution, respectively, we derive a differential equation of the conditional survival probability.In the next chapter, the Gerber-Shiu expected discounted penalty function of the Markovian risk model is considered, and we get the integro-differential equations for the Gerber-Shiu function. With the penalty function we derive the differential equation of the ruin probabilities, the deficits at ruin and the moment generating functions of the deficits.In the last chapter, we study the expected discounted dividend function under a barrier strategy. We derive the integro differential equations for the expected discounted dividend function, and get the differential equations of the expected discounted dividend function when the claims are in the Erlang(2), Erlang(n) and mixed-Erlang(2) distribution, respectively.