Knight不确定下带通胀的最优消费和投资模型研究

Study on Optimal Consumption and Portfolio with Inflation under Knightian Uncertainty

本文研究了投资者在Knight不确定下并带有通胀的最优消费和投资决策,其中区别含糊与含糊态度.首先,利用倒向随机微分方程理论,对Knight不确定投资者的α-maxmin期望效用进行了刻画.其次,利用动态规划原理,建立了最优消费和投资策略所满足的HJB方程,并给出了由三基金组成的修正的共同基金定理.最后,在定常相对风险厌恶(CRRA)效用的特殊情形下,获得了投资者最优消费和投资策略的显式解,并分析了含糊和通胀等因素对最优消费和投资决策的影响.

This paper studies the optimal consumption and portfolio choice problem of an investor who differentiates ambiguity and ambiguity attitude under the Knightian uncertainty （or ambiguity） and inflation. First, through the technique of backward stochastic differential equation （BSDE）, an investor＇s α-maxmin expected utility is characterized. Next, by using the dynamic programming prin- ciple, the HJB equation of optimal policies is derived, which deduces the modified mutual fund theorem consisting of three funds. Finally, in the special case of the constant relative risk-aversion utility, we derive the explicit expression of the optimal policy, and analyze the influence of ambiguity and inflation on optimal consumption and portfolio policies.