The Study Of Discrete Risk Models Under Randomized Dividend Strategy

When applying dividend strategies, the company has to observe the surplus level to make decisions on whether or not paying dividends. However, when the surplus level has a lot of fluctuations, the company may have to pay off dividends many times in a small time interval, and this will result in an increase of the company’s cost. In order to overcome this drawback, the experts present a randomized dividend strategy. The procedures in the business activities, such as income procedure, claim procedure and dividend procedure, are discrete procedures. It makes more sense to study the discrete risk model. In this paper, we will study the dividend, Geber-Shiu function and ruin probability of the discrete risk model under randomized dividend strategy. The structure and contents of this thesis are organized as follows:In Chapter 1, we simply introduce the background of the classical risk model and some definitions in this section. Then the research of the classical risk model in domestic and overseas will be given. Finally, we introduce the compound binomial risk model and the contents of this thesis.In Chapter 2, we will describe some concepts mentioned frequently, including generating function, convolution and Dickson-Hipp operator. Moreover, some symbol in the thesis will be presented.In Chapter 3, we will study the discrete Markov additive risk model under randomized dividend strategy. Firstly, we describe the risk model simply. Then the recursive formula of Gerber-Shiu function is derived by generating function method, so the ruin probability is also obtained. Finally, a numerical example for ruin probability will be given.In Chapter 4, a delayed claims discrete risk model under randomized dividend strategy will be considered. Using an auxiliary process and the generating function method, we obtain the expression for the expected discounted dividends function. Finally, we give a numerical example when the claim amounts are constants.