Optimal control strategy for dividend-payments in a risk model with stochastic premiums

We consider a discrete-time risk model. It is assumed that premiums received in each time period are mutually independent and identically distributed random variables, and 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 fixed point theory. We obtain some properties of the optimal dividend strategy, and offer high efficiency algorithms for obtaining the optimal strategy and the optimal value function.