Paper: arXiv 2412.00655

Authors: Mario Ghossoub, Qinghua Ren, Ruodu Wang

Abstract

We study risk sharing among agents with preferences modeled by heterogeneous distortion risk measures, who are not necessarily risk averse. Pareto optimality for agents using risk measures is often studied through the lens of inf-convolutions, because allocations that attain the inf-convolution are Pareto optimal, and the converse holds true under translation invariance. Our main focus is on groups of agents who exhibit varying levels of risk seeking. Under mild assumptions, we derive explicit solutions for the unconstrained inf-convolution and the counter-monotonic inf-convolution, which can be represented by a generalization of distortion risk measures.

Complexity vs Empirical Score

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

Why this score: The paper presents a rigorous theoretical exploration of counter-monotonic risk sharing and inf-convolutions for risk-seeking agents with non-concave distortion risk measures. However, it is purely mathematical without any empirical backtesting, financial datasets, or numerical simulations.

Research Flowchart

  flowchart TD
    A[Research Goal: Solve Risk Sharing & Pareto Optimality for Non-Risk-Averse Agents] --> B[Inputs: Heterogeneous Distortion Risk Measures & Group Risk Profiles]
    B --> C[Methodology: Apply Inf-Convolution Framework to Preferences]
    C --> D[Compute Unconstrained & Counter-Monotonic Inf-Convolutions]
    D --> E[Outcomes: Explicit Closed-Form Solutions for Optimal Allocations]
    E --> F[Key Finding: Representation via Generalized Distortion Risk Measures]

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6 of 78 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.