Optimal Risk Sharing under Distorted Probabilities

TL;DR

This paper derives explicit formulas for optimal risk sharing among agents with distortion risk measures, considering market frictions and third-party constraints, and finds that stop-loss sharing is optimal in certain cases.

Contribution

It extends existing results to unbounded risks and market frictions, providing explicit formulas for Pareto optimal allocations under distortion risk measures.

Findings

Stop-loss sharing is optimal for two agents with common distortion functions.

Explicit formulas for Pareto optimal allocations are derived.

Market frictions and third-party constraints are incorporated into the risk sharing model.

Abstract

We study optimal risk sharing among $n$ agents endowed with distortion risk measures. Our model includes market frictions that can either represent linear transaction costs or risk premia charged by a clearing house for the agents. Risk sharing under third-party constraints is also considered. We obtain an explicit formula for Pareto optimal allocations. In particular, we find that a stop-loss or deductible risk sharing is optimal in the case of two agents and several common distortion functions. This extends recent result of Jouini et al. (2006) to the problem with unbounded risks and market frictions.