Technical Note—An Unexpected Stochastic Dominance: Pareto Distributions, Dependence, and Diversification
研究发现，对于独立同分布且均值无限的帕累托随机变量，其加权平均在一阶随机占优意义上大于单个变量，意味着分散化反而比不分散更差，并导致风险价值（VaR）的超可加性。
Diversification is generally regarded as an efficient tool to reduce portfolio risks. In “An unexpected stochastic dominance: Pareto distributions, dependence, and diversification,” Chen, Embrechts, and Wang showed that the weighted average of independent and identically distributed (i.i.d.) Pareto random variables with infinite mean is larger than one such random variable in the sense of first-order stochastic dominance, and thus diversification is, surprisingly, worse than no diversification. The relation implies superadditivity of value-at-risk, a regulatory risk measure used in the finance and insurance sectors. The obtained relation also holds under some form of negative dependence.