Some Problems Of Dual Risk Model Under Linear Dividend

Since 1957, the dividend problem was ?rst introduced and discussed by De. Finetti in the discrete time model. From then on, the dividend problem has become one of the important topics in the study of actuarial science. The dividend problem of the risk model with the constant dividend boundary has been studied quite thoroughly in a lot of works.However, with the development of society and the change of times, the linear dividend boundary depending on the time is more meaningful than the constant dividend boundary.Especially, the risk model with the constant dividend boundary will eventually lead to bankruptcy with probability 1, but the risk model with the linear dividend barrier can overcome this defect. So, the classical risk model with the linear dividend strategy dates back to Gerber, who put it forward in 1974, and raises extensive attention of more and more scholars. Due to the classical risk model as the extension of the dual risk model. In recent years, researches on the dual risk model with a barrier dividend strategy have been increasingly concerned, but few of the discussions involving a linear dividend strategy have been given. We introduce constant interest, diffusion and random observation on the basis of the dual risk model with a linear dividend strategy, and study some dividend problems of this dual risk model. According to these research details, this paper is divided into four chapters:In Chapter 1, we introduce the research status and the structural arrangement in this paper.In Chapter 2, we discuss the perturbed dual risk model with constant interest and the linear dividend strategy. The expected discounted dividends payments and the moment generating function of the discounted dividend payments are studied, and the integrodifferential equations and some boundary conditions which they satis?ed are given.In Chapter 3, we consider the dual risk model with random observation time and the linear dividend strategy. We study the expected discounted dividends payments and ruin probability,and the integro-differential equations and some boundary conditions which they satis?ed are given.In Chapter 4, we discuss the perturbed dual risk model with random observation time and the linear dividend strategy. The integro-differential equations and some boundary conditions which the expected discounted dividends payments and ruin probability satis-?ed are given.