Study On The Portfolio Strategy Of Insurance Under The Two-Compound Poisson Model

Insurance investment is not only related to its healthy and steadily development, but has a significant effect on the normal operation of the national economy. So the reasonable operating of insurance capital, and scientific investing are particularly important. This thesis is based on the classic risk model, by taking the surplus capital being invested in order to improve profit and reduce ruin probability, a new type of practical risk model is proposed. For this type of new model, we study it mainly from these ways:In classical risk models and many extended risk models, we always assumpt that the arrival process and claim process are independent. But the fact is the more policies are sold, the more claims occur correspondingly. So the policy’s arrival is related to the occurrence of claims, we can regard claim process as a p-thinning process of arrival process. In chapter 3, we consider the risk model with investment and interference, the premiums and the claims follow the compound Poisson process, and claim process is a p-thinning process of arrival process. After analyzing the proposed model, under the expected value funds principles, the independent and stationary increment properties of the profit process are obtained. The upper-bounds of the ultimate ruin probability, its Lundberg inequality and integral-differential equations of the survival probability are also derived by martingale method.In chapter 4, we improve the model of investment to make more profit. The investment includes one riskless asset and one risky asset, which is more practically according with the development of the finance. In the first part, we consider the optimal investment strategy under the minimal ruin probability, by using the optimal control of the stochastic control theory, we set up the HJB equation of this risk model, and obtain the optimal invest approach in order to make the ruin probability being least; In the second part we study the optimal investment strategy under the maximal terminal expected utility. Introducing the expected exponential utility function, we set up the HJB equation, speculate and obtain the specific form of the solution. Especially for the premium following the exponential distribution case, we conclude the relationship of the optimal investment strategy and some factors such as risky asset volatility by numerical simulation, which make the study has more application value.In chapter 5, in order to diversify risk and stable income, according to Markowitz principle, we invested the fund to one risk-free bond and n kinds of risk assets. The optimal investment strategy is studied under the mean-variance principle, and solved by Lagrange multiplier method. This topic has pointed out a direction for the development of insurance company.