Robust Mean–Variance Portfolio Optimization: Mean–Variance–Variance Criterion Versus Mean–Variance–Standard Deviation Criterion
研究了动态投资组合优化问题，比较了均值-方差-方差准则和均值-方差-标准差准则，发现后者能解释有限股市参与现象。
ABSTRACT We study a dynamic portfolio optimization problem under the mean–variance–variance (M‐V‐V) criterion proposed by Maccheroni et al. It is an analogue of the Arrow–Pratt approximation to the well‐known smooth ambiguity model. Under the standard Black–Scholes framework, we derive fully explicit equilibrium investment strategies in which a DM's level of ambiguity, risk aversion, and ambiguity aversion are transparently captured. We find that the time horizon appears inconsistently in the objective function of the M‐V‐V criterion, in turn causing the equilibrium strategies to be nonmonotonic with respect to risk aversion. In response, we introduce a new mean–variance–standard deviation (M‐V‐SD) criterion to address this issue. Equilibrium strategies under the M‐V‐SD criterion exhibit an appealing feature of limited stock market participation which provides a theoretical justification to this phenomenon.