The Compound Poisson Risk Model Under A Mixed Dividend Strategy

In this paper, we consider a compound Poisson model under a mixed dividend strategy. The mixed dividend strategy is a combination of the threshold dividend strategy and the periodic dividend strategy. Given a positive threshold level b, whenever the surplus process attains the level b, dividends will be paid off continuously at a ratea(29)0. Furthermore, given a sequence of dividend decision times, whenever the observed surplus level atjZ is larger than b, the excess value will also be paid off as dividend. We study the expected discounted dividend payments before ruin and the Gerber-Shiu expected discounted penalty function. Some numerical examples are also presented. The structure and contents of this thesis are organized as follows:In Chapter 1, we introduced the research background and significance as well as the Compound Poisson risk model and the current research status of risk model with dividend policy.In Chapter 2, we introduce some concepts, formulas and properties that frequently used in the paper, including the definition of Laplace, partial fraction expansion,Dickson-Hipp operator and so on.In Chapter 3, we mainly introduce the compound Poisson risk model that considered the threshold dividend strategy and the periodic dividend strategy simultaneously.In Chapter 4, this is the core of our paper. Under the compound Poisson risk model with mixed dividend strategy, we devote to study the equations of the expected discounted dividend payments before ruin and the Gerber-Shiu expected discounted penalty function.At the same time,we display the process that how to obtain the explicit solution about the above two equations.In Chapter 5, in order to explain the results we have obtained in Chapter 4, we present some numerical results of the expected discounted dividend payments and the Gerber-Shiu expected discounted penalty function. Given the values of some parameters,we show several sets of figures directly present some properties of the expected discounted dividend payments and the Gerber-Shiu expected discounted penalty function.