Seminar Optimal risk sharing with infinite mean losses

Abstract

This paper studies optimal risk-sharing when losses exhibit infinite means, a situation where classical diversification and convex-order arguments can break down. We establish a generalized convex-order framework suitable for comparing heavy-tailed risks and show that, contrary to standard models, linear pooling may increase risk and be welfare-reducing. Motivated by practical limited-liability settings, we show that sharing only a capped portion of losses restores optimality, ensuring agents avoid certain bankruptcy while still benefiting from pooling. We characterise the optimal cap and show that limited-liability preferences lead to non-trivial sharing rules distinct from classical Arrow–Mossin insurance results. Numerical experiments with Pareto losses and dependence structures illustrate the optimal sharing threshold and highlight the influence of tail heaviness, wealth, risk aversion, and pool size.

This is joint work with Alfred Müller.