Optimal Control Policy Of Modified Standard Deviation Premium Principle Under Diffusion Model

Insurance company,as a financial institution,plays a very important role in national economic construction and social security.How to evade risks for policy-holders,effectively operate capital and ensure the stable operation of the financial system has become an important research topic for insurance company management.Under the modified standard deviation premium principle,this paper studies the optimal control strategy of insurance companies by using dynamic programming and HJB equation.That is to say,the optimal dividend and reinsurance strategies are obtained in the case of non-financing and financing to maximize the return of shareholders.The main work of this paper is as followsIn this paper,we discuss the problem of the optimal dividend about the proportional reinsurance and capital injection of the portfolio of insurance securities.particularly,the reinsurance premium is assumed to be calculated via modified standard deviation principle instead of variance principle.Under the principle of standard deviation premium,a proportional reinsurance diffusion model HJB equation based on the compound Poisson process is obtained.The optimization problem is studied in four parts according to whether capital injection is allowed and whether the dividend strategy is restricted.For these four cases,the expression of the value function and the expression and reinsurance strategy of the optimal dividend have been given.From the conclusion,we can see that The optimal control problem of unbounded dividend-sharing speed can be regarded as the optimal control problem of bounded dividend-sharing speed with the limit of ? ?.the optimal dividend strategy is a barrier strategy.The optimal risk cession ratio proportionally decreases with respect to the initial surplus.When the initial surplus exceeds the dividend boundary,the optimal risk cession ratio is constant.