基于跳跃扩散过程的保险资金最优投资模型研究

保险公司的盈余为跳跃扩散过程,保险人投资于债券和股票,且股票的价格服从跳跃扩散过程的最优投资组合。在均值-方差准则下通过随机最优控制方法,建立并求解保险资金投资模型的HJB方程,获得了保险资金最优投资模型和有效边界的闭式解,并进行了数值模拟。结果显示,投资于风险证券的资金量与初始资本金并不是简单的正比例关系。

Optimal Insurance Funds Investment Model Based On the Jump Diffusion Processes

The surplus of the insurance company follows the jump diffusion processes. The optimal portfolio will be achieved when the insurer invests its surplus in band and stock whose price follows jump diffusion processes. Under the mean variance principle, the HJB equation of insurance funds investment model and the optimal investment model and the efficient frontier have been researched in the paper. In the end, numerical simulations are performed.