Counter-monotonic Risk Sharing with Heterogeneous Distortion Risk Measures

TL;DR

This paper investigates risk sharing among agents with diverse distortion risk measures, including risk-seeking behaviors, providing explicit solutions for optimal allocations using generalized distortion measures.

Contribution

It introduces explicit solutions for risk sharing with heterogeneous distortion risk measures, including counter-monotonic allocations, extending existing models to risk-seeking agents.

Findings

Explicit solutions for unconstrained inf-convolution

Explicit solutions for counter-monotonic inf-convolution

Representation via generalized distortion risk measures

Abstract

We study risk sharing among agents with preferences modeled by heterogeneous distortion risk measures, who are not necessarily risk averse. Pareto optimality for agents using risk measures is often studied through the lens of inf-convolutions, because allocations that attain the inf-convolution are Pareto optimal, and the converse holds true under translation invariance. Our main focus is on groups of agents who exhibit varying levels of risk seeking. Under mild assumptions, we derive explicit solutions for the unconstrained inf-convolution and the counter-monotonic inf-convolution, which can be represented by a generalization of distortion risk measures.