模型不确定和极端事件冲击下带通胀的最优投资组合选择问题研究

本文研究了投资者在极端事件冲击下带通胀的最优投资组合选择问题, 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. 投资者在风险资产和无风险资产中进行投资. 首先, 利用Ito公式推导考虑通胀的消费篮子价格动力学方程, 其次由通胀折现的终端财富预期效用最大化, 对含糊厌恶投资者的最优期望效用进行刻画. 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式解. 最后, 通过数值模拟, 分析了含糊厌恶、风险厌恶、跳和通胀因素对投资者最优资产配置策略的影响.

An Investor's Optimal Portfolio with Rare Events and Model Uncertainty under Inflation

This paper is concerned with the optimal portfolio choice of an investor under the inflation and rare events impact, where the investor is aversive not only to the risk of loss but also to model uncertainty. An investor allocates his assets to the risky asset and the riskless asset. First, we obtain the dynamics of consumer-basket-price with inflation by using formula. Second, under maximizing the expected utility of intermediate consumption and terminal wealth discounted by inflation, the value function of ambiguity aversion investors is characterized. Through the dynamic programming principle, we derive the HJB equation satisfied by the value function of an investor's optimal consumption and portfolio. Third, applying market decomposition method to solving the HJB equation, the optimal consumption and portfolio policy for investors is obtained. Finally, the effect of the ambiguity aversion, risk aversion and inflation on an investor's optimal allocation strategy is analyzed by numerical simulation.