Paper: arXiv 2602.14223

Authors: Tim J. Boonen, Kenneth Tsz Hin Ng, Tak Wa Ng, Thai Nguyen

Abstract

We propose a peer-to-peer (P2P) insurance scheme comprising a risk-sharing pool and a reinsurer. A plan manager determines how risks are allocated among members and ceded to the reinsurer, while the reinsurer sets the reinsurance loading. Our work focuses on the strategic interaction between the plan manager and the reinsurer, and this focus leads to two game-theoretic contract designs: a Pareto design and a Bowley design, for which we derive closed-form optimal contracts. In the Pareto design, cooperation between the reinsurer and the plan manager leads to multiple Pareto-optimal contracts, which are further refined by introducing the notion of coalitional stability. In contrast, the Bowley design yields a unique optimal contract through a leader-follower framework, and we provide a rigorous verification of the individual rationality constraints via pointwise comparisons of payoff vectors. Comparing the two designs, we prove that the Bowley-optimal contract is never Pareto optimal and typically yields lower total welfare. In our numerical examples, the presence of reinsurance improves welfare, especially with Pareto designs and a less risk-averse reinsurer. We further analyze the impact of the single-loading restriction, which disproportionately favors members with riskier losses.

Complexity vs Empirical Score

  • Math Complexity: 7.5/10
  • Empirical Rigor: 3.0/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper provides a rigorous game-theoretic framework with theoretical closed-form derivations for Pareto and Bowley designs in P2P reinsurance. However, it lacks empirical backtesting on real-world insurance loss data, relying primarily on stylized numerical examples to illustrate welfare dynamics.

Research Flowchart

  flowchart TD
    A["Research Goal:<br>Design optimal P2P reinsurance contracts via game theory"] --> B["Inputs:<br>P2P pool risk profile & reinsurer risk tolerance"]
    B --> C["Game-Theoretic Modeling"]
    
    C --> D["Pareto Design:<br>Cooperative game yields multiple stable contracts"]
    C --> E["Bowley Design:<br>Leader-follower Stackelberg game yields unique contract"]
    
    D --> F["Analytical & Numerical Evaluation"]
    E --> F
    
    F --> G["Key Findings:<br>• Bowley contract is sub-optimal to Pareto<br>• Reinsurance boosts total welfare<br>• Single-loading favors riskier members"]

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3 of 100 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.