The Compound Poisson Risk Model With Random Gains And Periodic Dividend Strategy

Research on compound Poisson risk model and many generalized risk model mostly based on the following important conditions: the premium income is linear growth. However, the income of insurance company is not easy to be determined in real situation, and some insurance companies may have some large random income. In order to describe the stochastic income, this paper mainly studied the stage of dividend policy for insurance company and introduced compound Poisson risk model with random income, related to the Gerber-Shiu function of this model and the problem of surplus dividend. It mainly includes the calculation method of the expected discounted dividend payments, the determination of the optimal dividend policy and the calculating method for Gerber-Shiu function. In this paper, the structure and contents are arranged as follows:In Chapter 2, we mainly introduced several important concepts that will be used frequently,including Laplace transform, convolution, Dickson-Hipp operator and the definition and related properties of compound Poisson process.In Chapter 3, under the stage of dividend policy we introduced compound Poisson risk model with random income. This method mainly based on the Laplace transformation and its inverse transform. Meanwhile,by the construction of auxiliary function and combining with mathematics method, we got the recursive formula of Gerber-Shiu function. Finally, two numerical examples of computing Gerber-Shiu function are given in the special case.In Chapter 4, we consider the stage of dividend policy with the introduction of compound Poisson risk model for random income. Mainly using Laplace transformation and its inverse transform, the construction of auxiliary function and combining with mathematical methods,the bonus' present value is deduced and the determination of the optimality of dividend policy is also reached. Finally, two numerical examples are given in special circumstances.