Paper: arXiv 2510.18236

Authors: Mario Ghossoub, Qinghua Ren, Ruodu Wang

Abstract

We study Pareto-optimal risk sharing in economies with heterogeneous attitudes toward risk, where agents’ preferences are modeled by distortion risk measures. Building on comonotonic and counter-monotonic improvement results, we show that agents with similar attitudes optimally share risks comonotonically (risk-averse) or counter-monotonically (risk-seeking). We show how the general $n$-agent problem can be reduced to a two-agent formulation between representative risk-averse and risk-seeking agents, characterized by the infimal convolution of their distortion risk measures. Within this two-agent framework, we establish necessary and sufficient conditions for the existence of optimal allocations, and we identify when the infimal convolution yields an unbounded value. When existence fails, we analyze the problem under nonnegative allocation constraints, and we characterize optima explicitly, under piecewise-linear distortion functions and Bernoulli-type risks. Our findings suggest that the optimal allocation structure is governed by the relative strength of risk aversion versus risk seeking behavior, as intuition would suggest.

Complexity vs Empirical Score

  • Math Complexity: 8.5/10
  • Empirical Rigor: 1.0/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper provides a rigorous mathematical framework for analyzing Pareto-optimal risk-sharing among heterogeneous agents with distortion risk measures. However, it is purely theoretical with no empirical data analysis, backtests, or implementation code included.

Research Flowchart

  flowchart TD
    A["Research Goal: Determine Pareto-Optimal Risk Sharing<br/>with Heterogeneous Agents & Distortion Risk Measures"] --> B["Inputs: n Agents, Distortion Functions,<br/>Mixed Risk Attitudes & Total Risk X"]
    
    B --> C["Step 1: Reduce n-Agent System to 2-Agent System<br/>(Representative Risk-Averse vs. Risk-Seeking)"]
    
    C --> D["Step 2: Apply Infimal Convolution<br/>& Monotonicity Improvements"]
    
    D --> E["Step 3: Analyze Existence Conditions<br/>(Check Unbounded Value & Add Nonnegativity Constraints)"]
    
    E --> F["Outcomes: Optimal Allocations Characterized<br/>(Comonotonic for Averse, Counter-monotonic for Seeking)"]

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7 of 124 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.