The Optimal Policy for Insurance Company with Real Investment
保险公司实业项目投资策略研究

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".