Paper: arXiv 2510.19511

Authors: Jan Dhaene, Atibhav Chaudhry, Ka Chun Cheung, Austin Riis-Due

Abstract

This paper studies the mathematical problem of allocating payouts (compensations) in an endowment contingency fund using a risk-sharing rule that satisfies full allocation. Besides the participants, an administrator manages the fund by collecting ex-ante contributions to establish the fund and distributing ex-post payouts to members. Two types of administrators are considered. An ‘active’ administrator both invests in the fund and receives the payout of the fund when no participant receives a payout. A ‘passive’ administrator performs only administrative tasks and neither invests in nor receives a payout from the fund. We analyze the actuarial fairness of both compensation-based risk-sharing schemes and provide general conditions under which fairness is achieved. The results extend earlier work by Denuit and Robert (2025) and Dhaene and Milevsky (2024), who focused on payouts based on Bernoulli distributions, by allowing for general non-negative loss distributions.

Complexity vs Empirical Score

  • Math Complexity: 7.5/10
  • Empirical Rigor: 2.5/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper provides a formal theoretical extension of compensation-based risk-sharing mechanisms (e.g., tontines/P2P insurance) from Bernoulli claims to general non-negative loss distributions. While mathematically rigorous and clearly explained, it is entirely theoretical without empirical data, empirical backtests, or code execution.

Research Flowchart

  flowchart TD
    A[Research Goal: Actuarial fairness in compensation-based risk-sharing with active vs. passive administrators] --> B[Inputs: Ex-ante contributions & General non-negative loss distributions]
    B --> C[Model Formulation: Risk-sharing rule satisfying full allocation]
    C --> D[Mathematical Analysis: Evaluate active vs. passive administrator structures]
    D --> E[Outcome: General fairness conditions extending Bernoulli models to general losses]