Ruin Theory For Two Risk Models And Related Problems

More and more people are interested in Levy risk processes, recently. In this paper we go on to study this model. In Chapter 2 of this thesis, we study the ruin probability of a risk model driven by a subordinator and perturbed by a Brownian motion, and give a asymptotic behavior of ruin probability. In Chapters 3-4, we consider two risk models with two class of claims.The thesis is divided into four chapters according to contents:Chapter 1: In this chapter, firstly, we introduce the classical theory of risk models and the development of risk models. Secondly, we introduce the maim problems which are studied and the risk modles which are considered in this thesis.Chapter 2: In this chapter, we consider a risk model driven by a subordinator and perturbed by a Brownian motion, and get some asymptotic expression of ruin probability when the claim sizes have a heavy-tailed distribution.Chapter 3: In this chapter, we consider a risk model involving two independent class of calim processes, that is, we assume the two claim number processes are independent Poisson and generalized Erlang(n) processes, respectively. We give an integro-differential equations system which is satisfied by the Gerber-Shiu function and the expression of the Laplace transform of the Gerber-Shiu functions is obtained. In the last section of this chapter, when the generalized Erlang(n) processes is the generalized Erlang(2) processes, we obtain some generalized renewal equations which are satisfied by the Laplace transforms for the Gerber-Shiu functions.Chapter 4: In this chapter, we consider a risk model involving two independent class of insurance risks with fixed dividend strategy. We get the integro-differential equation for the moment generating function of total dividend discount expectations. We consider the solution of the integro-differential equation when the claim sizes have exponential distribution.