Optimal Dividend Strategies In Discrete-time Risk Model With Stochastic Premiums

We consider two new discrete-time risk models based on classical discretetime risk model. In the ?rst model,it is assumed that premiums received in each time period are mutually independent and identically distributed random variables; In the second model,the premiums received in each time period follow a Markov chain. Meanwhile we consider the capital injection which make the company never ruin. In this paper, the probability of claim occurrence in any time period is related to the premium received in corresponding period. We discuss the optimal dividend strategy. Our method is mainly to transform the value function and use ?xed point theory. We obtain some properties of the optimal dividend strategy, and o?er high e?ciency algorithms for obtaining the optimal strategy and the optimal value function. we can ?nd that the numerical calculation is consistent with the results of theoretical study.