A fixed point approach for computing actuarially fair Pareto optimal risk-sharing rules

Paper: arXiv 2303.05421

Authors: Fallou Niakh

Abstract

Risk-sharing is one way to pool risks without the need for a third party. To ensure the attractiveness of such a system, the rule should be accepted and understood by all participants. A desirable risk-sharing rule should fulfill actuarial fairness and Pareto optimality while being easy to compute. This paper establishes a one-to-one correspondence between an actuarially fair Pareto optimal (AFPO) risk-sharing rule and a fixed point of a specific function. A fast numerical method for computing these risk-sharing rules is also derived. As a result, we are able to compute AFPO risk-sharing rules for a large number of heterogeneous participants in this framework.

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 presents a strong theoretical framework using fixed point theory to compute actuarially fair Pareto optimal risk-sharing rules efficiently for large groups. However, it is primarily a mathematical and computational theory contribution lacking empirical backtesting or real-world market dataset validation.

Research Flowchart

  flowchart TD
    A[Goal: Compute Actuarially Fair Pareto Optimal<br>Risk-Sharing Rules for Large Groups] --> B[Inputs: Pool of Heterogeneous Participants<br>& Individual Risk Profiles]
    B --> C[Methodology: Establish 1-to-1 Correspondence<br>Between AFPO Rules & Fixed Point Function]
    C --> D[Numerical Computation: Apply Fast<br>Fixed Point Iteration Algorithm]
    D --> E[Outcome: Efficient Computation of<br>Fair & Optimal Risk-Sharing Rules]