Pareto Optimal Centralized Risk Sharing with Multiple Agents: Inclusivity and Fairness

2026-06-22

AI Summary

This study addresses the limitation of traditional Pareto optimality in multi-agent centralized risk-sharing problems, where certain participants may be inadequately represented, leading to imbalanced decisions. The authors propose a sequential optimization framework under endogenous prices and introduce the notion of “inclusive fair Pareto optimality,” which lies between classical Pareto optimality and Geoffrion’s proper Pareto optimality. This new concept requires that each agent be represented exactly once within a finite sequence of optimizations. By integrating multi-objective optimization, risk measures (such as Expected Shortfall), and pricing functionals, the paper establishes the equivalence between inclusive fair Pareto optimality and equilibrium sequential optimization. The theoretical validity and fairness of the proposed approach are demonstrated through an Expected Shortfall-based example.

Abstract

This paper studies centralized risk sharing with endogenous prices. Multiple policyholders transfer risks to a central insurer through indemnity decisions, while prices are determined by pricing functionals applied to ceded risks. The resulting problem is multiobjective, with Pareto optimality as the natural efficiency criterion. We show that classical Pareto optimality may fail to reveal whether all agents are represented in a balanced decision process that scalarized objectives may assign zero weight to some agents, and group aggregates may obscure individual risk positions. Motivated by bilateral Pareto characterizations through sequential optimization, we introduce inclusive and fair Pareto optimality, a representation-based refinement requiring every agent to appear exactly once, either individually or as part of a group, in a finite ordered sequence of optimizations. Our main result proves equivalence between this concept and balanced sequential optimization, placing it between Geoffrion-proper Pareto optimality and classical Pareto optimality. An illustrative example demonstrates the framework using the Expected Shortfall.

Problem

• Pareto optimality
• risk sharing
• fairness
• inclusivity
• multiobjective optimization

Innovation

• Pareto optimality
• risk sharing
• inclusivity
• fairness
• sequential optimization