Abstract:

Standing at the viewpoint of the decision maker of an insurance company, this paper investigates the reinsurance-investment strategies for an insurance
company with option of real estate investment. We assume that the insurance company has the possibility of investing in one real project, which will cost the insurance company a fixed amount of wealth and will bring in a fixed income rate as return. The insurance company may also invest its wealth in a Black-Scholes financial market with one risk-free asset (bond, or bank account) and one risky asset (stock), and may reduce its risk exposure or increase its premium using proportional reinsurance contract. The insurance company's main objective is the minimal ruin probability and the corresponding optimal strategy (including the timing of real investment, proportion of reinsurance and the amount of money invested in risky asset). With methodology of combined stochastic
control and optimal stopping, we obtain the value function and the optimal strategy explicitly. Finally, we analyze the optimal strategy numerically to illustrate our results. It is shown that: (a) The investment threshold of real project is mainly affected by the project's return; its connection with the cost of the real investment is vague. A higher real ivestment return leads to a lower investment threshold. (b) The real investment threshold is lower in a bear market than that in a bull market.

Key words: real investment, risky-asset investment, proportional reinsurance, ruin probability, combined stochastic control and optimal stopping problem