保险公司实业项目投资策略研究

考虑保险公司实业项目投资问题. 假定1)保险公司可以选择在某一时刻投资一实业项目(Real investment), 该项投资可以为保险公司带来稳定的资金收入而不影响其风险;2)保险公司可以将盈余资金投资于证券市场, 该市场包含一风险资产.目标是通过最小化破产概率来确定保险公司实业项目投资时间和风险资产的投资金额.运用混合随机控制-最优停时方法,得到值函数的半显式解, 进而得到保险公司的最佳投资策略: 以固定金额投资证券市场; 当保险公司盈余高于一定额度(称为投资门槛)时进行项目投资, 并降低风险资产投资金额.最后采用数值算例分析了不同市场环境下投资门槛与投资金额, 投资收益率之间的关系. 结果表明:1)项目投资所需金额越少、收益率越高, 则项目投资的门槛越低;2)市场环境较好时(牛市)项目的投资门槛提高, 保险公司应较多的投资于证券市场; 反之, 当市场环境较差时(熊市)投资门槛降低,保险公司倾向于实业项目投资.

THE OPTIMAL POLICY FOR INSURANCE COMPANY WITH REAL INVESTMENT

In this paper the problem of real investment for an insurance company is studied. Assume that the insurer may choose to invest in one real project, which would cost her a fixed amount of wealth and bring her fixed income rate as return, and that the company may also invest in financial market, including a risky asset. The main objective of this paper is to obtain the minimal ruin probability and its corresponding optimal strategy (including the real investment time and the amount invested in the risky asset). With methodology of mixed stochastic control-optimal stopping, the value function and the optimal strategy are given semi-explicitly. These results show that: (1) the insurer should invest in real project once the value of surplus is higher than a certain threshold (called the {real-investment threshold}); (2) before and after the real investment time the company should invest different fixed amount in the risky asset, the risky asset investment after the real investment is less than that before the real investment. Finally, numerical examples are given to illustrate the results given above. The numerical example shows that (1) less investment cost and higher repayment result in a lower threshold; (2) the real investment threshold in ``bullish market" is higher than that in ``bearish market".