Some Class Of Ruin Probability Problems In The Dual Model

This paper mainly studies the dual model which is the continuation of the risk theory.In recent years,the dual risk model has made great breakthroughs under the research of the scholars,but a few man attentions on the omega model and the capital exchange model.So we will solve the ruin probability and give the related conclusion under the Omega model and capital exchange model in this paper,respectively.The main structure of this paper is as follows:In Chapter 1,at first,we simply introduce the background of the risk theory and its development.Then,we introduce some related knowledge.Finally,we present the main content of this paper and the main result of my research.In chapter 2,some dual models are presented briefly.In chapter 3,we assume that the surplus process for dual model is a com-pound Poisson process perturbed by a Brown motion and also we propose a Omega model for a Jump-Diffusion Process.We study the resulting bankrupt-cy probability for compound Poisson risk model with exponential claim size,deriving the corresponding parameters and obtaining the expression of ruin probability.Finally,the paper proposes the bankrupt ruin under the special cases and give some numerical examples.In chapter 4,we consider a capital-exchange agreement of two companies ruin probability and total expected discounted funding under the threshold dividend dual model.Then we derive the differential equation for it.Finally,we explain the relationship between the coefficients and the solution of differential equations by numerical analysis method.