方差保费准则下最优分红、注资和再保险策略

Optimal dividend,capital injection and reinsurance strategies with variance premium principle

本文研究保险公司的最优分红、注资和再保险策略问题.保险公司可以通过再保险安排控制自身的风险暴露,它与再保险公司在方差保费准则下采用不同的参数进行费率定价.保险公司管理者也可以通过分红或注资控制公司资产,控制过程会消耗比例交易费和固定交易费.破产前分红现值与注资现值期望之差视为保险公司的价值.在最大化公司价值目标下,利用脉冲控制理论,本文找到最优的分红、注资和再保险策略及公司价值的最大值.

This paper considers the combined optimal dividend, capital injection and reinsurance strategies for an insurance company. The proportion reinsurance is taken as a risk control, the variance principle is adopted by the insurer and the reinsurer with different parameter respectively. Furthermore, the insurer can control its surplus by paying dividends and injecting capitals, which incur both proportional and fixed costs. The value of the company is defined as the difference between the expected discounted dividends and the expected discounted capital injections until the time of bankruptcy. To maximize the value of the company, by solving the impulse problem, we obtain explicit solutions for value function and optimal strategy.