Robust Optimal Risk Sharing and Risk Premia in Expanding Pools

TL;DR

This paper investigates how optimal risk sharing and associated risk premia behave as the pool of agents grows, considering both standard and ambiguity-averse preferences, with explicit asymptotic results.

Contribution

It introduces a robust approach to risk sharing that accounts for model uncertainty, providing explicit asymptotic limits and convergence rates.

Findings

Risk premia decrease as pool size increases.

Robust certainty equivalents incorporate ambiguity aversion.

Explicit asymptotic limits for risk sharing in large pools.

Abstract

We consider the problem of optimal risk sharing in a pool of cooperative agents. We analyze the asymptotic behavior of the certainty equivalents and risk premia associated with the Pareto optimal risk sharing contract as the pool expands. We first study this problem under expected utility preferences with an objectively or subjectively given probabilistic model. Next, we develop a robust approach by explicitly taking uncertainty about the probabilistic model (ambiguity) into account. The resulting robust certainty equivalents and risk premia compound risk and ambiguity aversion. We provide explicit results on their limits and rates of convergence, induced by Pareto optimal risk sharing in expanding pools.