Classical Risk Model With Interference With The Regular Interest Rate Bonus

Dividends payment problem is a very important task in the study of insurance and finance. How should the dividends be paid to the shareholders, if the aim is to maximize the expectation of the discounted dividends until possible ruin of the company? This problem goes back to De Finetti, who solved it in the discrete time in 1957. From then on, lots of thesis began to study dividends payment problem. For classical risk process model perturbed by diffusion or with interest, many aspects have been studied quite thoroughly, and we obtain many beautiful results. But in fact, for one aspact, the surplus process is influenced by diffusion, for another, the insurance company will receive interest. This paper is based on the predecessors, a standard Brownian motion and a constant interest r>0 are added in the classical risk process, so the surplus process becomes to be the classical risk process model with diffusion and interest, that is: Based on this model, we will discuss kinds of dividends payment problems according to the Barrier and Threshold strategy.According to the contents, this paper is divided into three chapters:Chapter 1 is the introduction. In this part, the study situation and background of dividends payment problems is briefly introduced, which is prepared for the content of Chapter 2 and Chapter 3.In Chapter 2, we will discuss the dividends payment problems with the Barrier strat-egy. What is the Barrier strategy? This is for a given positive parameter b, no dividends are paid whenever the surplus does not exceed b, but whenever the surplus exceed b, the part exceeding b will be paid to shareholders. This chapter specifically includes:First for 00 whenever the modified surplus is above b. The structure of this chapter is the same with Chapter 2, but the conclusions are different.