Optimal Dividend And Injection Strategies With Two Reinsurers Company Participated

This paper considers the combined optimal dividend,capital injection and reinsurance strategies for an insurance company,in which we have two reinsurers participating.In order to control the risk,the insurer and two reinsurers adopt the variance premium principle with different parameters.First,to avoid bankruptcy,the insurance company will receive capital injections,but during the process,it also will occur some fixed transaction costs and proportional taxes.For the goal of minimize the transaction cost,we use the dynamic programming method to find the optimal strategy.Furthermore,we also give numerical analysis.Secondly,we assume that the reinsurance has not only injection,but also dividend.Similarly,we take the transaction cost in the process into consideration.The value of the company is defined as the difference between the expected discounted dividends and the expected discounted capital injections until the time of bankruptcy.To maximize the value of the company,by solving the impulse problem,we obtain explicit solutions for value function and optimal strategy.This paper is divided into four chapters:The first chapter introduces the research background,research status at home and abroad and research contents.In the second chapter,we study the minimum of transaction cost.capital injection.The following is the main content:first,we make a model,leading up diffusion risk model;in the second,we adopt mixed ratio reinsurance.We give the objective function and we use the dynamic programming method to solve it.In the last,we give the optimal injection strategies and numerical analysis of relevant parameters.In the third chapter,we study the maximum of the value of the company capital injection and dividend.The following is the main content:fist,we make a model,leading up the drift diffusion process.In the second,we adopt mixed ratio reinsurance and give the objective function.And by solving the impulse problem we obtain explicit solutions for value function and optimal dividend and injection strategies.The last chapter is a summary and evaluation of the article.