Research On The Wealth Management Optimization Of Insurance Company

The issue on the wealth management optimization of insurance company has been developed rapidly, since Cramer studied the bankruptcy question by using stochastic process. The theory of the wealth management not only enriches the financial theory, but also leads to the communication of finance, insurance and mathematics. It is very important to minimize the ruin probability for insurance company, at the same time, the wealth’s maximization is the managers’ optimization objective.In the paper, the mathematical models are established with earnings process obeying the Poisson-jump, the compound Poisson-jump and the Levy process, where the ruin probability, optimal reinsurance problem and optimal investment-reinsurance problem are studied by using martingale method and stochastic control method, the equations satisfied by the ruin probability and the survival probability are obtained and the optimal investment-reinsurance strategy are given. The dissertation of the paper is organized as follows:(1) The ruin probability of insurance company are studied by using martingale method and stochastic control method, under the model whose earnings process meets Poisson-jump and earnings process is Levy process. The partial differential equations of the ruin probability for insurance company are obtained, respectively assumed that the interest rate is normal, the interest rate is stochastic and earnings process is with Markov modulation parameters.(2) The optimal reinsurance problems with earnings process being Poisson-jump and earnings process being Levy process are studied under the aims with the minimum ruin probability, by using martingale method and stochastic control method. The partial differential equations on existence probability are given.(3) The optimal investment-reinsurance problems are investigated with earnings process meeting Poisson-jump and earnings process meeting compound Poisson-jump, by using stochastic dynamic programming control method, under the aims with maximizing the expected utility of terminal wealth condition. The maximized expected exponential utility optimal investment-reinsurance strategy are obtained.