基于注资-阀值分红的随机微分投资-再保博弈  

Stochastic Differential Investment-Reinsurance Games with Capital Injection-Threshold Dividend

作　　者：孙宗岐[1] 陈志平[2] SUN Zong-qi;CHEN Zhi-ping(Department of Mathematics, Xi＇an Siyuan University, Xi＇an 710038, China;school of Mathematics and Statistics, Xi＇an Jiaotong University, Xi＇an 710049, China)

机构地区：[1]西安思源学院高数教研室,陕西西安710038 [2]西安交通大学数学与统计学院,陕西西安710049

出　　处：《数学的实践与认识》2017年第21期108-121,共14页Mathematics in Practice and Theory

基　　金：国家自然科学基金(71371152);陕西省教育厅2016年度自然科学专项基金(2016JK2150)

摘　　要：为了更好地反映模型风险对保险公司金融策略的影响,考虑了存在模型风险时,保险公司的最优投资-再保-注资-阀值分红策略问题.在分红与注资总量的贴现值之差的期望最大化的准则下,使用零和随机微分博弈理论建立了保险公司的随机微分博弈模型,通过求解HJBI方程得到了最优投资-再保-注资-阀值分红策略的显式解.最后在有模型风险和无模型风险两种不同情形下,通过数值算例分析了保险公司金融策略之间的差异,为保险资金的管理提供了重要的决策指导.To better reflect the impact of model risk on the insurance company＇s finan- cial strategy, we investigate the optimal problem of investment-reinsurance-capital injection- threshold dividend when model risk exist. Based on the criterion of maximizing the expected total present value on the difference between threshold dividend and capital injection, the model is utilized by using zero stochastic differential game principle, and the optimal poli- cies are obtained through solving the HJBI equation. The closed-form strategies of optimal investment-reinsurance-capital injection-threshold dividend have been derived. Finally, in the case of model risk and model-free risk, the difference between financial strategies of insurance companies is analyzed by numerical examples, Providing important decision-making guidance for the management of insurance capital.

关 键 词：随机微分博弈 HJBI方程 投资策略 再保险策略 注资-阀值分红 模型风险 

分 类 号：F840.3[经济管理—保险] O211.63[理学—概率论与数理统计]