极端事件冲击下含糊厌恶投资者的最优投资组合选择问题

Ambiguity aversion investor's optimal portfolio with rare events

研究了在极端事件冲击下含糊厌恶投资者的最优投资组合问题,其中,投资者不仅对损失风险是厌恶的而且对模型不确定也是厌恶的.首先,利用随机微分方程理论,对含糊厌恶投资者的最优期望效用进行刻画.其次,利用动态规划原理,建立最优消费和投资策略所满足的HJB方程.再次,利用市场分解的方法解出HJB方程,获得投资者最优消费和投资策略的显示解.最后,通过数值模拟,分析了含糊厌恶、风险厌恶和跳对投资者最优投资组合选择问题的影响.

The optimal portfolio choice of an investor with ambiguity aversion under rare event impact was studied ,where the investor is aversive not only to the risk of loss but also to model uncertainty .First ,the optimal expected utility of ambiguity aversion investors was characterized using the theory of stochastic differential equations . Second , the value function of an investor＇s optimal consumption and portfolio satisfying the HJB equation was derived through the dynamic programming principle .Third ,the optimal consumption and portfolio policy for investors was obtained by applying market decomposition method to solving the HJB equation . Finally , the effect of the ambiguity aversion , risk aversion and jump on investors＇ optimal portfolio choice was analyzed by numerical simulation .