Research On Insurance Company 's Investment And Reinsurance Strategy Under Jump Diffusion

The insurance company plays an important role in the financial system. The insurance com-pany helps the insurers to reduce their risks. Meanwhile, the insurance company earns the profit and increases the efficiency of the financial system. The management of the insurance company faces the important issue on how to choose the appropriate strategies to achieve their goals. This paper established the optimal control models for the insurance company in a multi-dimentional jump-diffusion market. In the paper, the control policies are associated with the reinsurance rate, investment strategy, etc. The objectives of the management refer to maximization of the company value and minimization of the risk.This paper in the first chapter introduces the main research method and the status quo of the insurance companies to invest in the jump-diffusion market and buy scale reinsurance, in the second chapter presents the basic preliminary knowledge used by the model in this paper. In the third chapter, the insurance company bought a proportional reinsurance to spread part of risk, at the same time, the assets invested in the capital market, and risk assets using multidimensional jump diffusion model. The goal is to choose the optimal reinsurance scale and investment strategy made the company reached the maximum value at a lixed time, and find out the corresponding value function. In this paper, the multidimensional problem is transformed into a one-dimensional problem, and then the HJB equation of the optimal problem obtains by the dynamic programming principle, finally we obtain the optimal reinsurance scale and investment strategy. Then we draw some figures and give graphical analysis.In the fourth chapter, the insurance company buys proportional reinsurance and assets in the multidimensional jump-diffusion capital market, and the goal is to choice the optimal investment and proportional reinsurance strategy to make the final variance minimized when the expectation of the final wealth of the insurance company is constant, which is the risk minimized, and the minimum variance is obtained. In order to solve this problem, using though Lagrangc duality theorem, looking the problem of the mean-variance as optimal control problem with equality constraint, using though a Lagrange multiplier is introduced to convert the original problem into an optimal control problem without equality constraint, we can take advantage of the dynamic programming method to solve. Finally, with regard to the optimal Lagrangc multipliers have been seeking the solution of the original problem. Finally we analyze the result.In the fourth chapter, the insurance company buys proportional reinsurance and assets in the multidimensional jump-diffusion capital market, and here we consider the possibility of reinsur-ance companies default, Then the insurance company’s surplus process at time t requires to be considered from two cases, that is default before time t and default after time t. We use the indi-cator function to wrilte both cases as a stochastic differential equation. The goal is to choose the optimal reinsurance scale and investment strategy made the company reached the maximum value at a fixed time. and find out the corresponding value function, The solving process references the method in the three chapter.The conclusion and prospect in chapter six gives the inadequate of the paper and the future research direction.