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Dominance between combinations of infinite-mean Pareto random variables

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  • Yuyu Chen
  • Taizhong Hu
  • Ruodu Wang
  • Zhenfeng Zou

Abstract

We study stochastic dominance between portfolios of independent and identically distributed (iid) extremely heavy-tailed (i.e., infinite-mean) Pareto random variables. With the notion of majorization order, we show that a more diversified portfolio of iid extremely heavy-tailed Pareto random variables is larger in the sense of first-order stochastic dominance. This result is further generalized for Pareto random variables caused by triggering events, random variables with tails being Pareto, bounded Pareto random variables, and positively dependent Pareto random variables. These results provide an important implication in investment: Diversification of extremely heavy-tailed Pareto profits uniformly increases investors' profitability, leading to a diversification benefit. Remarkably, different from the finite-mean setting, such a diversification benefit does not depend on the decision maker's risk aversion.

Suggested Citation

  • Yuyu Chen & Taizhong Hu & Ruodu Wang & Zhenfeng Zou, 2024. "Dominance between combinations of infinite-mean Pareto random variables," Papers 2404.18467, arXiv.org.
    • Handle: RePEc:arx:papers:2404.18467
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    File URL: http://arxiv.org/pdf/2404.18467
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