Static Comparative Analysis of Portfolio Selection under Ambiguity Aversion

传统投资组合理论假设风险的概率分布已知，但现实中投资者往往面临“模糊性”——即概率分布本身未知的不确定性。从直觉上来说，更多的模糊厌恶会减少对不确定资产的需求，但事实并非总是如此。本文采用Klibanoff、Marinacci和Mukerji (2005)提出的“平滑模糊厌恶模型”，该模型通过区分模糊性与模糊态度，并分阶段应用期望效用理论——先对一阶分布计算期望效用，再对二阶信念进行加权。当函数为线性时，模型退化为标准期望效用理论；而当为凹函数时，则刻画了模糊厌恶行为，此时无法简化为单一复合分布。通过研究一个静态双资产(无风险资产 + 模糊性风险资产)组合问题，其中风险资产的收益率服从依赖连续未知参数的分布，在此框架下，本文推导出“增强模糊厌恶会降低风险资产需求”的充分条件，一个满足这些充分条件的例子是，当不确定资产回报的可能分布可以按照其单调似然比进行排序。研究结果揭示了模糊性在投资组合选择中的复杂作用，对不确定性下投资者行为的传统假设提出了挑战。Traditional portfolio theory assumes that the probability distribution of risk is known, but in reality, investors often face “ambiguity”—uncertainty where the probability distribution itself is unknown. Intuitively, greater ambiguity aversion would reduce demand for ambiguous assets, yet this is not always the case. This paper adopts the “smooth ambiguity aversion model” proposed by Klibanoff, Marinacci, and Mukerji (2005), which distinguishes between ambiguity (beliefs) and ambiguity attitude (preferences), and applies expected utility theory in two stages—first computing expected utility over first-order distributions, then weighting second-order beliefs. When the weighting function is linear, the model reduces to standard expected utility theory; when the function is concave, it captures ambiguity-averse behavior, precluding reduction to a single compound distribution. By studying a combination problem of static dual assets (risk-free asset + ambiguous risk asset) in which the rate of return of risk asset follows the distribution dependent on continuous unknown parameters , under this framework, this paper derives the sufficient condition that “enhanced fuzzy aversion reduces demand for risky assets”. An example that meets these sufficient conditions is when the possible distribution of uncertain asset returns can be ranked according to its monotonic likelihood ratio. The findings reveal the complex role of ambiguity in portfolio selection and challenge traditional assumptions about investor behavior under uncertainty.