基于Hamilton-Jacobi-Bellman方程求解保险业最优投资策略

在经典复合泊松模型中,保险公司将资金投入一个风险投资过程和一个无风险投资过程.当索赔的分布确定后,运用随机控制中的HJB方程最小化保险公司的破产概率,在已知投资规模或投资组合的情况下求解二者中的另一项,进而得到最优投资策略并讨论各种策略的运用对破产概率的影响.解决保险公司的投资资金分配问题,在实际应用中具有一定的参考价值.

Hamilton-Jacobi-Bellman Equation for Optimal Investment Strategy

Assuming that the reserve of an insurance company follows a Cramer-Lundberg process,that The company invests its income into one risky asset and one riskless asset,and that the claim size distribution is given, the HJB equation was applied to minimize the ruin probability of the insurance company. Among the capital amount and optimal portfolio, if anyone is known, the other one can be determined. The optimal investment strategy is obtained. Finally, we discuss how different strategies influent the ruin probabilities. These results can be applied in actual operations.