Study On Dividend Problem For The Risk Processes With Intersection Delayed Claims

The study of discrete time risk model has always been the hot topic in financial insurance,and introducing the dependent structure in the model has more practical significance.In this article we consider discrete time interaction risk models with dividend barrier and delayed claims under constant interest rates and stochastic interest rate,in which two dependent classes of business are introduced.Each main claim in one class in the claims process may cause a by-claim in the other class and by-claim may be delayed to the next time with a certain probability.By introducing three auxiliary risk processes,difference equation and its solution satisfied by the expected present value of dividend payments are obtained.Finally a numerical example is given for two kinds of special claims distribution.Numerical results are also provided to illustrate the impact of the company's initial surplus and delayed claims on the expected present value of dividends.This thesis is divided into four chapters.Chapter 1.In this chapter,we first review the discrete time risk model with delayed claims and constant dividend barrier under constant interest rates and stochastic interest rate,respectively.Then we introduce some related definitions and propositions in the discrete time risk model as well as some research results in recent years.Chapter 2.In section 1,we mainly introduce the basic structure for the discrete time risk model with dividend barrier and intersection delayed claims.In section 2,by introducing three auxiliary risk processes,we derive the difference equations for the expected present value of dividend payments prior to ruin by using the probability generating function and the differential equation theory.Chapter 3.In this chapter,we focus on considering the dividend strategy of risk model with intersection delayed claim under stochastic interest rates.We assume that the market interest rates follow a time-homogeneous Markov chain with finite state space.Then the difference equations for the expected present value of dividend payments with boundary condition prior to ruin and the expression of the solution are derived.Chapter 4.In the last chapter,we mainly consider two special claims distribution: one is the truncated geometrical distribution such that it's probability generating function is a polynomial,and the other case assumes claims have finite support such that probability generating function can be expressed as a ratio of two polynomials with certain conditions.We obtain simple expressions for the expected present value of the dividend payments for these two special cases.The corresponding numerical examples are also provided.