OPTIMAL DIVIDEND-PENALTY STRATEGIES FOR INSURANCE RISK MODELS WITH SURPLUS-DEPENDENT PREMIUMS

This paper concerns an optimal dividend-penalty problem for the risk models with surplus-dependent premiums.The objective is to maximize the difference of the expected cumulative discounted dividend payments received until the moment of ruin and a discounted penalty payment taken at the moment of ruin.Since the value function may be not smooth enough to be the classical solution of the HJB equation,the viscosity solution is involved.The optimal value function can be characterized as the smallest viscosity supersolution of the HJB equation and the optimal dividend-penalty strategy has a band structure.Finally,some numerical examples with gamma distribution for the claims are analyzed.