Optimal Risk-Sharing Rules in Network-based Decentralized Insurance

TL;DR

This paper explores optimal risk-sharing mechanisms in decentralized insurance networks, characterizing fair risk distribution among connected agents and linking it to graph Laplacian properties.

Contribution

It introduces a novel model for risk-sharing on networks, deriving optimal signed linear rules and connecting equal-sharing cases to graph Laplacians.

Findings

Characterized optimal risk-sharing rules in network-based insurance.

Established a link between equal-sharing risk rules and graph Laplacian.

Provided illustrative examples demonstrating the theoretical results.

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.