Optimal Risk-Sharing Rules in Network-based Decentralized Insurance

Paper: arXiv 2602.05155

Authors: Heather N. Fogarty, Sooie-Hoe Loke, Nicholas F. Marshall, Enrique A. Thomann

Abstract

This paper studies decentralized risk-sharing on networks. In particular, we consider a model where agents are nodes in a given network structure. Agents directly connected by edges in the network are referred to as friends. We study actuarially fair risk-sharing under the assumption that only friends can share risk, and we characterize the optimal signed linear risk-sharing rule in this network setting. Subsequently, we consider a special case of this model where all the friends of an agent take on an equal share of the agent’s risk, and establish a connection to the graph Laplacian. Our results are illustrated with several examples.

Complexity vs Empirical Score

• Math Complexity: 8.0/10
• Empirical Rigor: 1.5/10
• Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper provides strong theoretical derivations extending optimal risk-sharing rules to general network topologies using graph Laplacians. However, it is entirely theoretical with no empirical data analysis, real-world backtesting, or historical loss validation.

Research Flowchart

  flowchart TD
    A[Research Goal: Derive Optimal Decentralized Risk-Sharing Rules on Networks] --> B[Model Setup: Agents as Nodes, Friends as Edges]
    B --> C[Constraint: Actuarially Fair & Local Risk-Sharing Only]
    C --> D[Methodology: Derive Optimal Signed Linear Risk-Sharing Rule]
    D --> E[Special Case: Equal Risk Allocation Among Friends]
    E --> F[Mathematical Connection to Graph Laplacian Matrix]
    F --> G[Outcomes: Explicit Formulas & Network Examples]