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根据监管规定,保险公司必须提存一定水平的准备金。鉴于此,保险公司必须保持盈余不低于这个准备金水平。将保险公司盈余首达该准备金水平的时刻定义为“破产”时刻,以最小化“破产”概率为目标;假设保险公司可购买比例再保险,其盈余过程由扩散模型刻画且盈余按连续复利方式计算利息,其中利力为常数;借助随机动态规划方法,通过求解相应的HJB方程得到了最优值函数与最优比例再保险策略的解析式。最后给出了经济解释与数值算例。
According to regulatory requirements, insurers must deposit a certain level of reserves. In view of this, insurers must keep a surplus of not less than this reserve level. The moment when the insurance company’s earnings reach the reserve level is defined as the moment of “bankruptcy”, with the objective of minimizing the probability of “bankruptcy”; assuming that insurance companies can buy proportional reinsurance, the surplus process is characterized by a diffusion model and the surplus Interests are calculated in a continuous compound way, of which the force is constant. By means of stochastic dynamic programming, the analytical solution of the optimal value function and the optimal proportional reinsurance strategy is obtained by solving the corresponding HJB equation. Finally, the economic explanation and numerical examples are given.