标题： 分散化与随机优势：当所有鸡蛋都放在一个篮子里时 显示英文标题

标题： Diversification and Stochastic Dominance: When All Eggs Are Better Put in One Basket

摘要： 传统观念警告不要“把所有的鸡蛋放在一个篮子里”，多样化被广泛认为是降低风险的可靠策略。 然而在某些极端条件下，这种直觉不仅失效，甚至会逆转。 本文通过识别新的情境来探讨这种逆转，这些情境中多样化反而增加了风险。 我们的主要结果——一个篮子定理——提供了充分条件，使得独立风险的加权平均值在第一阶随机优势的意义上大于一个将所有风险集中在随机选择的一个风险上的混合模型。 我们的框架处理了非同分布的风险，并包括了新的例子，如无限均值的离散帕累托变量和圣彼得堡彩票。 我们进一步表明，这些逆转并非孤立的异常现象，而是更广泛现象的边界情况：多样化总是会增加超过小阈值的可能性，在特定条件下，这种局部效应会扩展为全局效应，导致第一阶随机优势。 显示英文摘要

摘要： Conventional wisdom warns against "putting all your eggs in one basket," and diversification is widely regarded as a reliable strategy for reducing risk. Yet under certain extreme conditions, this intuition not only fails - it reverses. This paper explores such reversals by identifying new settings in which diversification increases risk. Our main result - the one-basket theorem - provides sufficient conditions under which a weighted average of independent risks is larger, in the sense of first-order stochastic dominance, than a corresponding mixture model that concentrates all exposure on a single risk chosen at random. Our framework handles non-identically distributed risks and includes new examples, such as infinite-mean discrete Pareto variables and the St. Petersburg lottery. We further show that these reversals are not isolated anomalies, but boundary cases of a broader phenomenon: diversification always increases the likelihood of exceeding small thresholds, and under specific conditions, this local effect extends globally, resulting in first-order stochastic dominance.