Research On The Problem Of Dividend In Risk Models

In this paper,we investigate the optimal dividend and financing strategy problems with reinsurance and a terminal value.The competent authorities of the company make the best strategy to maximize the expectation of the cumulative discounted value of the dividends and the terminal value minus capital injection.Among them,we mainly consider the optimal control of insurance companies using excess-loss reinsurance and non-cheap proportional reinsurance respectively.In the two model,the principle of expectation is applied to the premium calculation principle of reinsurance.We solve the optimal control problem by constructing the suboptimal model,that is,one is no capital injection,and the other is the insurance company's capital injection at the time of ruin.The optimal policy control problem is solved by using approximate diffusion and dynamic programming principles,and the corresponding HJB equation and verification theorem.