An Optimal Control Problem In A Risk Model With Stochastic Premiums And Periodic Dividend Payments

In this paper,a discrete-time risk model is considered. We assume that the premium received in each time interval is a positive real-valued random variable,and the sequence of premiums is a Markov chain. In any time interval the proba-bility of a claim occurrence is related to the premium received in the corresponding period. We discuss control strategies for dividends paid periodically to the share-holders under two cases: absence and presence of ceiling restriction for dividend rates. We provide high efficiency algorithms and some properties for the optimal control strategies by transforming the value function and using fixed point the-ory. In addition, we offer some numerical calculation to achieve optimal dividend strategy. We show that under the absence of a ceiling of dividend restriction,the optimal strategy is a conditional barrier strategy given the current state of the Markov chain. Under the presence of a ceiling for dividend restriction, the optimal strategy is a conditional threshold strategy.