多样化偏好与风险态度
Diversification Preferences and Risk Attitudes
AI总结：
本文研究多样化与风险厌恶之间的关系，通过分析不同多样化形式与风险厌恶概念的联系，探讨了弱和强风险厌恶的区别，以及不同风险对之间的多样化偏好与风险态度的关系。
摘要：
投资组合多样化是现代金融的基石，而风险厌恶是决策理论的核心；这两个概念历史悠久且基础稳固。我们通过研究不同形式的多样化如何对应于风险厌恶的概念来探讨它们的联系。我们聚焦于弱风险厌恶与强风险厌恶的经典区别，并考虑不同风险对之间的多样化偏好与风险态度的关系。在弱连续性条件下且不假设偏好完全性的情况下，对于反单调性和相同分布的风险对，多样化暗示弱风险厌恶，而对于交换性风险对，多样化等同于强风险厌恶。对于独立风险对的多样化到弱风险厌恶的推论需要更强的连续性。我们进一步提供了澄清各种多样化偏好与风险态度之间关系的结果和例子，特别是阐明了许多推论的一向性质。
英文摘要：
Portfolio diversification is a cornerstone of modern finance, while risk aversion is central to decision theory; both concepts are long-standing and foundational. We investigate their connections by studying how different forms of diversification correspond to notions of risk aversion. We focus on the classical distinctions between weak and strong risk aversion, and consider diversification preferences for pairs of risks that are identically distributed, comonotonic, antimonotonic, independent, or exchangeable, as well as their intersections. Under a weak continuity condition and without assuming completeness of preferences, diversification for antimonotonic and identically distributed pairs implies weak risk aversion, and diversification for exchangeable pairs is equivalent to strong risk aversion. The implication from diversification for independent pairs to weak risk aversion requires a stronger continuity. We further provide results and examples that clarify the relationships between various diversification preferences and risk attitudes, in particular justifying the one-directional nature of many implications.
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