Periodic Dividend Optimization Problem In A Markovian Environment Model Under The Control Of Survival Probability

This paper considers the periodic dividend optimization problem in a Marko-vian environment model with interest under the constraints of survival probability.Assume that the premium received in each time interval is a positive real-valued random variable,and the premium sequence has a markov property.The occur-rence of a claim at any time is closely related to the premium received in the corresponding unit time.The optimal policies is considered in two cases:absence and presence of ceiling restriction for dividend rates.First,under the control of survival probability,We obtain the constraint thresholds.Then,by transforming the value function and applying the fixed point theorem,we provide some prop-erties and an algorithm of the optimal dividend strategies under the constraint conditions.Finally,we provide numerical examples to explain algorithm.Our results show that the optimal strategy is a conditional band strategy under the absence of ceiling restriction for dividend rates;and the optimal strategy is a Multi-threshold strategy under the presence of ceiling restriction for dividend rates.Besides,no matter whether the dividend rates have ceiling restriction or not,the largest cumulative expectation of dividends is negatively correlated with the strength of survival probability constraint,this is in line with the actual oper-ation of the company.Our conclusions can provide a theoretical support for the company's operation and development.