Pareto-Optimal Peer-to-Peer Risk Sharing with Robust Distortion Risk Measures

TL;DR

This paper characterizes Pareto-optimal risk-sharing arrangements in decentralized peer-to-peer markets using robust distortion risk measures, emphasizing tail risk assessment and proposing alternatives to centralized flood insurance markets.

Contribution

It provides a novel characterization of Pareto-optimal allocations under non-convex distortion risk measures and applies it to decentralized flood risk insurance.

Findings

Pareto-optimal allocations depend on tail risk assessments.

Decentralized risk sharing can be an effective alternative to centralized insurance.

Numerical analysis with historical flood data illustrates the proposed arrangements.

Abstract

We study Pareto optimality in a decentralized peer-to-peer risk-sharing market where agents' preferences are represented by robust distortion risk measures that are not necessarily convex. We obtain a characterization of Pareto-optimal allocations of the aggregate risk in the market, and we show that the shape of the allocations depends primarily on each agent's assessment of the tail of the aggregate risk. We quantify the latter via an index of probabilistic risk aversion, and we illustrate our results using concrete examples of popular families of distortion functions. As an application of our results, we revisit the market for flood risk insurance in the United States. We present the decentralized risk sharing arrangement as an alternative to the current centralized market structure, and we characterize the optimal allocations in a numerical study with historical flood data. We conclude with an in-depth discussion of the advantages and disadvantages of a decentralized insurance scheme in this setting.