通胀环境下股价波动率具有奈特不确定的最优消费与投资问题

本文在通胀环境和连续时间模型假设下，研究股票价格波动率具有奈特不确定对投资者的最优消费和投资策略的影响．首先在通胀环境和股票价格波动率具有奈特不确定的条件下，建立最优消费与投资问题的随机控制数学模型，得到了最优消费与投资所满足的HJB方程，并在常相对风险厌恶效用的情形下，获得最优化问题值函数的显式解．其次在通胀环境中当股价波动率具有奈特不确定时，得到了含糊厌恶的投资者是基于股价波动率的上界作出决策，并给出了投资者的最优投资和消费策略．最后在给定参数的条件下，对所得结果进行数值模拟和经济分析．

On Study of Optimal Consumption and Portfolio with Knightian Uncertainty of Stock Price Volatility Under Inflation

This paper studies the effect of the Knightian uncertainty of stock price volatility on an investor＇ s optimal consumption and portfolio with a continuous - time model under inflation. Firstly, a stochastic optimal control model for the optimal consumption and investment decision problem is established under the environment of Knightian uncer tainty of stock price volatility and inflation, Then through the HJB equation of the optimal consumption and portfolio, an explicit expression of the valued function of optimization problem in the case of constant relative risk - aversion （CRRA） utility is obtained. Thirdly, we get that the make - decision of an ambiguity averse investor is based on the upper bound of stock price volatility uncertainty under the environment of inflation. Finally, the numerical simulation and its economic analysis are provided.