道德风险影响下的保险最优投资研究
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引用本文:张芯芮,王亚洁,荣喜民.道德风险影响下的保险最优投资研究[J].经济数学,2020,(1):34-42
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作者单位
张芯芮,王亚洁,荣喜民 (天津大学 数学学院天津 300350) 
中文摘要:在考虑道德风险的情况下,以均值方差准则为目标研究保险人最优投资问题. 假设保险盈余过程服从C-L模型,金融市场上存在一种无风险资产和一种风险资产可供投资,其中风险资产的价格过程服从几何布朗运动.在纯道德风险保险契约设计中,借鉴相关研究对努力水平和效用化努力成本的假设,量化道德风险对盈余过程的影响. 在均值-方差目标下,建立保险人最优投资问题的广义Hamilton-Jacobi-Bellman(HJB)方程,给出保险人时间一致的均衡投资策略和价值函数. 结果显示累计索赔比例参数越大, 公司对最优努力水平越敏感, 采取措施降低道德风险有利于公司收益提升;努力成本参数越大, 公司会降低努力水平减少支出,避免损失.
中文关键词:最优投资  道德风险  动态均值-方差准则  随机控制理论
 
The Optimal Investment Strategy under Moral Hazard
Abstract:This paper studies an insurance optimal investment model on the condition of moral hazard under mean-variance criterion. In insurance industry, moral hazard can undermine economic benefits. What is worse, the company could go bankrupt. Therefore, quantification of the moral hazard is apparently significant. We assume the surplus of insurers is described by C-L model. The insurers invest in a risk-free asset and a risk asset whose price follows the geometric Brownian motion model. According to the research on the optimal insurance contract under pure moral hazard, this paper considers assumptions of the effort level and effort cost of utility. Regarding to the conclusion, the moral hazard is quantified through the surplus process. Based on mean-variance criterion, an extended Hamilton-Jacobi-Bellman (HJB) equation of the equilibrium value function is established in the time-consistent framework. The final expression for the time-consistent investment strategy and the optimal value function are derived by the stochastic control theory. The analysis illustrates that the higher the parameter of cumulative claim rate is, the more sensitive the effort level is. Taking measure to reduce the moral hazard is beneficial for the return. Meanwhile, the increase of the effort cost parameter leads to lower effort level to avoid cost.
keywords:optimal investment  moral hazard  dynamic mean-variance criterion  stochastic optimal control
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