Optimal Control Policy Of The Insurance Company

The insurance company plays an important role in the financial system. The in-surance company helps the insurers to reduce their risks. Meanwhile, the insurancecompany earns the profit and increases the e?ciency of the financial system. The man-agement of the insurance company faces the important issue on how to choose theappropriate strategies to achieve their goals. This paper established the optimal controlmodels for the insurance company and work out the optimal control policy as well asthe optimal value function via the HJB-SDE methods. In the paper, the control policiesare associated with the reinsurance rate, dividends payout, equity issuance, etc. Ac-cording to the theory of corporation management, the objectives of the managementrefer to maximization of the returns of the shareholders, maximization of the com-pany value and minimization of the ruin probability of the insurance company. Thesestochastic control problems can be solved e?ectively via the stochastic analysis meth-ods, such as HJB-SDE methods, Ito? and Girsanov methods. The contributions in thispaper are: establishing the more practical models and working out the optimal valuefunction and the optimal control policies for the new model. I believe that it will bepretty helpful for the management of the insurance company to make their decisions.This is the first time to consider the financing process. The equity issuance is animportant approach for the company to earn profit as well as reduce risk. The prob-lem is solved by using the HJB-SDE methods ?exibly. The method to judge whetherthe insurance company needs equity issuance is given. We also establish the optimalreturn function and the optimal control policies for the two types of insurance com-panies. Moveover, the fixed and the proportional transaction costs are both taken intoconsideration. How to balance the risk and return is a hot issue in financial research,the optimal control policy of the insurance company with solvency constraints is dis-cussed. The existence and monotony of the dividend barrier is proved in this paper.The correlations between the capital market and the insurance company are considered and the e?ects of the correlations on the optimal control policies are established in thelast section.The problems solved in this paper are referred to the urgent need in the insurancepractice. Solving these problems required the integrated use of financial mathematics,insurance, probability, stochastic analysis and optimization. The conclusions in thispaper have important roles in guiding China's insurance industry development and thestability of the financial system.