Technical Note—An Unexpected Stochastic Dominance: Pareto Distributions, Dependence, and Diversification

Yuyu Chen (), Paul Embrechts () and Ruodu Wang ()
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Yuyu Chen: Department of Economics, University of Melbourne, Melbourne, Victoria 3010, Australia
Paul Embrechts: RiskLab, Department of Mathematics and ETH Risk Center, ETH Zurich, 8092 Zurich, Switzerland
Ruodu Wang: Department of Statistics and Actuarial Science, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada

Operations Research, 2025, vol. 73, issue 3, 1336-1344

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.

Keywords: Decision Analysis; Pareto distributions; diversification effect; risk pooling; first-order stochastic dominance (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:inm:oropre:v:73:y:2025:i:3:p:1336-1344

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