Research On Ruin Problems In The Risk Model With Stochastic Premiums And Dependence

The compound Poisson risk model has been widely investigated since it has beenproposed. As everyone knows, there are two important assumptions that premium rate isa liner function of time and claim amount is independence with the inter-claim time. Inthis case, the risk model becomes simply, but it far different with certain practicalcircumstances. Thus the risk model with random premium and the dependence riskmodel are proposed respectively. As an important risk measure tool, the Gerber-Shiufunction has been widely used in the ruin theory, and many ruin related problems can bereduced to the evaluation of the Gerber-Shiu function. In this thesis, we will study theruin problems in the dependent risk model with random premium with using theGerber-Shiu function.Firstly, the risk theory is simply introduced about its background, main researchresults and its promotion. We present the main content of this text in the end of thischapter.In Section2, in view of the main contents in this paper, we introduce the FMGcopula function、Gerber-Shiu function and related theoretical knowledge.In Section3, we consider a risk model with stochastic premiums. Moreover, weassume that the claim inter-arrival times and claim sizes are dependent. Under thishypothesis, a dependence structure between the claim sizes and claim inter-arrival timesis introduced though a Farlie-Gumbel-Morgenstern copula. We derive theintegro-differential equation and Laplace transform and defective renewal equation forGerber-Shiu discount penalty function. An explicit expression for the Laplace transformof the discount penalty function is obtained for claim sizes having an exponentialdistribution.In Section4, in view of the above research results, we carry on the numericalsimulation. Through the numerical simulation, we explain the above conclusion, andverify the correctness of the conclusions in this paper.