Paper: arXiv 2302.04034

Authors: Jean-Gabriel Lauzier, Liyuan Lin, Ruodu Wang

Abstract

We address the problem of sharing risk among agents with preferences modelled by a general class of comonotonic additive and law-based functionals that need not be either monotone or convex. Such functionals are called distortion riskmetrics, which include many statistical measures of risk and variability used in portfolio optimization and insurance. The set of Pareto-optimal allocations is characterized under various settings of general or comonotonic risk sharing problems. We solve explicitly Pareto-optimal allocations among agents using the Gini deviation, the mean-median deviation, or the inter-quantile difference as the relevant variability measures. The latter is of particular interest, as optimal allocations are not comonotonic in the presence of inter-quantile difference agents; instead, the optimal allocation features a mixture of pairwise counter-monotonic structures, showing some patterns of extremal negative dependence.

Complexity vs Empirical Score

  • Math Complexity: 8.5/10
  • Empirical Rigor: 2.5/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper presents a rigorous theoretical framework for risk sharing using non-monotone and non-convex distortion riskmetrics, deriving explicit Pareto-optimal allocations for measures like Gini deviation and inter-quantile differences. However, it is purely theoretical without empirical backtesting or real-world data application.

Research Flowchart

  flowchart TD
    A[Research Goal: Characterize Pareto-Optimal Risk Sharing for Non-Monotone/Non-Convex Distortion Riskmetrics] --> B[Input: Risk/Variability Measures<br/>Gini, Mean-Median, Inter-Quantile Difference]
    B --> C[Methodology: General & Comonotonic Risk Sharing Frameworks]
    C --> D[Computational Optimization: Solve Pareto Allocations for Specific Variability Metrics]
    D --> E[Finding 1: Complete Characterization of Pareto-Optimal Allocations]
    D --> F[Finding 2: Inter-Quantile Difference yields Non-Comonotonic Allocations with Pairwise Counter-Monotonic Structures]