Ruin Probability And Optimal Control Policy Of The Insurance Risk Model

Insurance company plays an increasingly important role in the financial institutions. Besides, the competition of insurance company has becoming more and more intense. The growth mode of insurance company can not be sustained only if depending on insurance claims the difference. The insurance company, In fact, has a large number of internal cash flow. The management of the insurance company faces important issue on how to choose the appropriate investment strategies to achieve their goals.Three more in line with the market situation and the economic significance of the risk models are established, and the optimal control policy as well as the optimal value function by the HJB methods is worked out. The main research work is as follows.1. The single type of insurance risk model with variable ruin limit is considered. Although the ruin probability of this model is not easy to obtain, the upper bound of the ruin probability inequality is given finally. The inequality provides a powerful tool for risk management of insurance system, and has a certain guiding significance for the insurance company managers how to choose their operation strategy.2. Considering that the insurance company through continuous purchase reinsurance controls their business risk, a certain proportion of surplus capital is invested in the capital market. In fact, in our country, the insurance company is not allowed to put all premiums for risk investment. Therefore, a fixed proportion of total earnings to invest in the market risk have more realistic significance.3. On the assumption that there is a correlation between the capital market change and the insurance company capital change, by using the method of HJB-variations inequalities, the explicit expression for optimal control strategy as well as the optimal ruin probability function is obtained. Finally, some of the quantitative analysis of the effect of the correlation is discussed.