模糊厌恶下的最优投资与最优保费策略

保险公司的投资决策与保费收取决策至关重要.由于金融市场复杂性与风险性等特点,保险公司对金融市场的模型估计不可避免的会存在模糊性.因此在金融市场存在模糊性下研究保险公司的最优投资和最优保费策略会更加贴近现实.假设保险公司对金融市场的模型估计会存在模糊性,而保险公司对自己的模型由于其长时间的应用、经营和检验将不会存在模糊性.在模糊厌恶下,在最大化保险公司终端财富期望效用的目标下,给出了保险公司的最优投资和保费策略的解析解并得到了值函数具体的形式.结果显示:对金融市场模糊厌恶下求得的最优策略与不考虑模糊性下所求得的最优策略会存在联系,且金融市场的模糊性会对最优策略有明显的影响.

Optimal investment and premium policies with ambiguity aversion

It is of great importance to consider the investment policies and premium collections for insurers. Because of the complexity and risky of the financial market, the model of the financial market may prone to ambiguity. Hence, it is more realistic to investigate the optimal investment and premium control for insurers with consideration of the existence of ambiguity in the financial market. Intuitively, the insurance company will consider the ambiguity only exists in the financial market, while the surplus process of the insurance company will be considered completely correct due to its long-time applying, operating and testing. Under the assumption of above, the closed-form expressions for the optimal investment policy, the optimal premium control policy and the value function are obtained with maximizing the expected utility of the terminal company's wealth and with ambiguity aversion. It is concluded that there is a relationship on the optimal investment policies between considering the ambiguity aversion and without considering the ambiguity for the financial market. And the impacts of the ambiguity on optimal policies are significant.