The Research On The MAP Risk Model With The Problem Of Dividends And Bankruptcy

Since Asmussen introduced the Markov modulated process into the risk model,the risk model with Markov modulation has been widely studied because of its more realistic in describing the uncertainty of the model.This kind of risk model is usually in continuous time,and continuous observation is difficult to implement in practice.In this paper,Markov arrival process is introduced on the basis of Markov modulated risk model,which makes the model more reasonable.And we mainly discuss the expected discounted penalty function and the total expected discounted dividend.Through the Sine method to calculate the ruin probability.We obtain some results about ruin probability.the main ideas of these are as follows:In Chapter 1,we simply introduce the background of the risk theory and its development.Then,we present the main work of this paper and the main result of my research.In Chapter 2,we mainly introduce preliminary of the Sine function and some risk models about this work.In Chapter 3,we study the integro-differential equations of the expected discounted penalty function under The Markovian arrival risk model.Due to the complexity of the equation,we do not obtain the explicit expressions.In this chapter,we get the numerical solution of the expected discounted penalty function by using the Sine numerical calculation.Under the Sinc numerical calculation,the problem of ruin probability is discussed.In Chapter 4,on the basis of the Chapter 3,We consider the expected discounted dividend amount under the threshold dividend policy to satisfy the integral differential equation,and we do not get the exact solution.By using the Sine method,we obtain the numerical calculation solution of the expected discounted dividend total.Finally,the numerical example are discussed.In Chapter 5,We also consider the total expected discounted dividend under a constant threshold barrier and get its the Integro-differential equation with the perturbed Markovian arrival risk model.But we do not get its exact solution.We also show the Sine numerical method to deduce its numerical solution.Finally.we give some numerical examples,and discuss the influence of interference coefficient for the amount of dividends.