Journal of Applied Probability· 2026Q2
Stochastic dominance for linear combinations of infinite-mean risks
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- Q2SCImago
- 2026year
Short summary
A new sufficient condition is established for comparing linear combinations of independent, identically distributed infinite-mean risks, showing that smaller weight vectors (in the majorization sense) lead to stochastically larger combinations within a novel class of heavy-tailed distributions.
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Key points
- Establishes a sufficient condition for stochastic dominance of linear combinations of i.i.d. infinite-mean random variables.
- Introduces a new class of heavy-tailed distributions where smaller majorization-ordered weight vectors yield stochastically larger risk combinations.
- Extends the analysis to compound Poisson sums and stable distributions.
AI-generated from the title and abstract; the full text is not read.
Abstract
Abstract We establish a sufficient condition for comparing linear combinations of independent and identically distributed infinite-mean random variables under the usual stochastic order. We introduce a new class of distributions that includes many commonly used heavy-tailed models and show that within this class, a linear combination of random variables is stochastically larger when its weight vector is smaller in the sense of majorization order. We proceed to study the case where each random variable is a compound Poisson sum and demonstrate that if the stochastic dominance relation holds, the summand of the compound Poisson sum belongs to our new class of distributions. Additional discussions are presented for stable distributions.
The authors' abstract, as published at the source. Journal of Applied Probability, 2026 · DOI ↗
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Field: Management Science and Operations Research
Management Science and Operations ResearchDecision Sciences