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Stochastic dominance for super heavy-tailed random variables

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  • Yuyu Chen
  • Seva Shneer

Abstract

We introduce a class of super heavy-tailed distributions and establish the inequality that any weighted average of independent and identically distributed super heavy-tailed random variables stochastically dominates one such random variable. We show that many commonly used extremely heavy-tailed (i.e., infinite-mean) distributions, such as the Pareto, Fr\'echet, and Burr distributions, belong to the class of super heavy-tailed distributions. The established stochastic dominance relation is further generalized to allow negatively dependent or non-identically distributed random variables. In particular, the weighted average of non-identically distributed random variables stochastically dominates their distribution mixtures. Applications of these results in portfolio diversification, goods bundling, and inventory management are discussed. Remarkably, in the presence of super heavy-tailedness, the results that hold for finite-mean models in these applications are flipped.

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  • Yuyu Chen & Seva Shneer, 2024. "Stochastic dominance for super heavy-tailed random variables," Papers 2408.15033, arXiv.org.
    • Handle: RePEc:arx:papers:2408.15033
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