Paper: arXiv 2404.03783

Authors: Muqiao Huang, Ruodu Wang

Abstract

We establish a profound connection between coherent risk measures, a prominent object in quantitative finance, and uniform integrability, a fundamental concept in probability theory. Instead of working with absolute values of random variables, which is convenient in studying integrability, we work directly with random loses and gains, which have clear financial interpretation. We introduce a technical tool called the folding score of distortion risk measures. The analysis of the folding score allows us to convert some conditions on absolute values to those on gains and losses. As our main results, we obtain three sets of equivalent conditions for uniform integrability. In particular, a set is uniformly integrable if and only if one can find a coherent distortion risk measure that is bounded on the set, but not finite on $L^1$.

Complexity vs Empirical Score

  • Math Complexity: 8.5/10
  • Empirical Rigor: 1.5/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: This paper presents a strong theoretical advance linking coherent risk measures to probability theory’s uniform integrability using heavy mathematical proofs. However, it is entirely theoretical with no empirical data, backtesting, or code, making empirical rigor and reproducibility intentionally low.

Research Flowchart

  flowchart TD
    A[Research Goal: Connect Coherent Risk Measures <br>to Uniform Integrability UI] --> B[Input: Random Losses & Gains <br>in L1 Space]
    B --> C[Method: Analyze Financial Risk via <br>Coherent Distortion Risk Measures]
    C --> D[Compute: Folding Score Tool to Transform <br>Absolute Values to Gains/Losses]
    D --> E[Outcome: 3 Sets of Equivalent <br>Conditions for UI]
    E --> F[Key Finding: Set is UI iff Bounded by a <br>Coherent Distortion Risk Measure Non-Finite on L1]

Cited References (30)

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0 of 30 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.