Paper: arXiv 2409.05103

Authors: Mario Ghossoub, Michael B. Zhu, Wing Fung Chong

Abstract

We study Pareto optimality in a decentralized peer-to-peer risk-sharing market where agents’ preferences are represented by robust distortion risk measures that are not necessarily convex. We obtain a characterization of Pareto-optimal allocations of the aggregate risk in the market, and we show that the shape of the allocations depends primarily on each agent’s assessment of the tail of the aggregate risk. We quantify the latter via an index of probabilistic risk aversion, and we illustrate our results using concrete examples of popular families of distortion functions. As an application of our results, we revisit the market for flood risk insurance in the United States. We present the decentralized risk sharing arrangement as an alternative to the current centralized market structure, and we characterize the optimal allocations in a numerical study with historical flood data. We conclude with an in-depth discussion of the advantages and disadvantages of a decentralized insurance scheme in this setting.

Complexity vs Empirical Score

  • Math Complexity: 8.0/10
  • Empirical Rigor: 6.0/10
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper provides a rigorous mathematical framework for Pareto-optimal peer-to-peer risk sharing using non-convex robust distortion risk measures. It balances advanced theoretical derivations with a concrete empirical application to historical US flood insurance data, contrasting centralized vs. decentralized market structures.

Research Flowchart

  flowchart TD
    A[Research Goal: Characterize Pareto-Optimal P2P Risk Sharing under Robust Distortion Risk Measures] --> B[Theoretical Framework: Model Non-Convex Preferences & Probabilistic Risk Aversion Index]
    B --> C[Analytical Derivation: Characterize Optimal Risk Allocations based on Aggregate Risk Tail Assessments]
    C --> D[Empirical Application: US Flood Insurance Market P2P Alternative]
    E[(Data Inputs: Historical US Flood Risk Data)] --> D
    D --> F[Numerical Simulation & Optimization]
    F --> G[Key Outcomes: Optimal Allocation Models & Feasibility Analysis of Decentralized vs. Centralized Insurance]

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3 of 86 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.