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An unexpected stochastic dominance: Pareto distributions, dependence, and diversification

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  • Yuyu Chen
  • Paul Embrechts
  • Ruodu Wang

Abstract

We find the perhaps surprising inequality that the weighted average of independent and identically distributed Pareto random variables with infinite mean is larger than one such random variable in the sense of first-order stochastic dominance. This result holds for more general models including super-Pareto distributions, negative dependence, and triggering events, and yields superadditivity of the risk measure Value-at-Risk for these models.

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  • Yuyu Chen & Paul Embrechts & Ruodu Wang, 2022. "An unexpected stochastic dominance: Pareto distributions, dependence, and diversification," Papers 2208.08471, arXiv.org, revised Mar 2024.
    • Handle: RePEc:arx:papers:2208.08471
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    Cited by:

    1. Yuyu Chen & Paul Embrechts & Ruodu Wang, 2024. "Risk exchange under infinite-mean Pareto models," Papers 2403.20171, arXiv.org.
    2. Yuyu Chen & Ruodu Wang, 2024. "Infinite-mean models in risk management: Discussions and recent advances," Papers 2408.08678, arXiv.org, revised Oct 2024.
    3. Yuyu Chen & Taizhong Hu & Ruodu Wang & Zhenfeng Zou, 2024. "Dominance between combinations of infinite-mean Pareto random variables," Papers 2404.18467, arXiv.org, revised Nov 2024.

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