Paper: arXiv 2404.18467

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.

Complexity vs Empirical Score

  • Math Complexity: 8.5/10
  • Empirical Rigor: 2.0/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper is highly mathematical, using advanced probability theory (majorization order, stochastic dominance) and complex proofs, but lacks any empirical backtesting or implementation details, focusing purely on theoretical properties of infinite-mean distributions.

Research Flowchart

  flowchart TD
  A["Research Goal:<br/>Diversification effect for<br/>infinite-mean Pareto models"]
  B["Methodology:<br/>Majorization Order & Stochastic Dominance"]
  C["Inputs:<br/>iid extremely heavy-tailed<br/>Pareto random variables"]
  D["Computation:<br/>Analyze portfolios of size n<br/>using FSD conditions"]
  E{"Generalization check"}
  F["Key Finding:<br/>More diversified portfolios<br/>strictly increase FSD"]
  G["Outcome:<br/>Diversification benefit<br/>independent of risk aversion"]

  A --> B
  B --> C
  C --> D
  D --> E
  E -- Yes --> F
  F --> G

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and 26 more
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  2. General Proof that Diversification Pays (1967) — link
  3. Uncertainty and the size distribution of rewards from innovation (2000) — link
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  23. Technical Note—An Unexpected Stochastic Dominance: Pareto Distributions, Dependence, and Diversification (2024) — link
  24. Risk exchange under infinite-mean Pareto models — → 2403.20171
  25. Some remarks on the effect of risk sharing and diversification for infinite mean risks — → 2411.10139
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2 of 34 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.