Paper: arXiv 2407.16099

Authors: Mario Ghossoub, Qinghua Ren, Ruodu Wang

Abstract

In risk-sharing markets with aggregate uncertainty, characterizing Pareto-optimal allocations when agents might not be risk averse is a challenging task, and the literature has only provided limited explicit results thus far. In particular, Pareto optima in such a setting may not necessarily be comonotonic, in contrast to the case of risk-averse agents. In fact, when market participants are risk-seeking, Pareto-optimal allocations are counter-monotonic. Counter-monotonicity of Pareto optima also arises in some situations for quantile-optimizing agents. In this paper, we provide a systematic study of efficient risk sharing in markets where allocations are constrained to be counter-monotonic. The preferences of the agents are modelled by a common distortion risk measure, or equivalently, by a common Yaari dual utility. We consider three different settings: risk-averse agents, risk-seeking agents, and those with an inverse S-shaped distortion function. In each case, we provide useful characterizations of optimal allocations, for both the counter-monotonic market and the unconstrained market. To illustrate our results, we consider an application to a portfolio choice problem for a portfolio manager tasked with managing the investments of a group of clients, with varying levels of risk aversion or risk seeking. We determine explicitly the optimal investment strategies in this case. Our results confirm the intuition that a manager investing on behalf of risk-seeking agents tends to invest more in risky assets than a manager acting on behalf of risk-averse agents.

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, highly technical theoretical framework for counter-monotonic risk allocations using distortion risk measures and Choquet integrals. While it offers solid academic novelty and rigorous mathematical derivations, it lacks empirical backtesting or real-world data validation.

Research Flowchart

  flowchart TD
    A["Research Goal: Characterize Pareto-Optimal Allocations<br/>under Counter-Monotonicity Constraints"] --> B["Inputs: Common Distortion Risk Measures<br/>& Aggregate Market Uncertainty"]
    B --> C["Analyze Preference Settings:<br/>1. Risk-Averse<br/>2. Risk-Seeking<br/>3. Inverse S-Shaped"]
    C --> D["Derive Analytical Characterizations<br/>for Constrained & Unconstrained Markets"]
    D --> E["Application: Portfolio Choice Problem<br/>for Portfolio Manager & Clients"]
    E --> F["Key Outcome: Risk-seeking allocations are counter-monotonic;<br/>Risk-seeking managers invest significantly more in risky assets"]

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5 of 56 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.