Efficiency in Pure-Exchange Economies With Risk-Averse Monetary Utilities

Mario Ghossoub; Michael B. Zhu

doi:10.1111/mafi.70006

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Efficiency in Pure-Exchange Economies With Risk-Averse Monetary Utilities

Journal article

Peer reviewed

Efficiency in Pure-Exchange Economies With Risk-Averse Monetary Utilities

Mario Ghossoub and Michael B. Zhu

Mathematical finance, Vol.36(1), pp.99-117

01/01/2026

DOI: 10.1111/mafi.70006

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Abstract

We study Pareto efficiency in a pure-exchange economy where agents' preferences are represented by risk-averse monetary utilities. These coincide with law-invariant monetary utilities, and they can be shown to correspond to the class of monotone, (quasi-)concave, Schur concave, and translation-invariant utility functionals. This covers a large class of utility functionals, including a variety of law-invariant robust utilities. Given that Pareto optima exist and are comonotone, we provide a crisp characterization thereof in the case of law-invariant positively homogeneous monetary utilities. This characterization provides an easily implementable algorithm that fully determines the shape of Pareto-optimal (PO) allocations. In the special case of law-invariant comonotone-additive monetary utility functionals (concave Yaari-dual utilities), we provide a closed-form characterization of Pareto optima. As an application, we examine risk-sharing markets where all agents evaluate risk through law-invariant coherent risk measures, a widely popular class of risk measures. In a numerical illustration, we characterize PO risk-sharing for some special types of coherent risk measures.

Business & Economics

Business, Finance

Economics

Mathematical Methods In Social Sciences

Mathematics

Mathematics, Interdisciplinary Applications

Physical Sciences

Science & Technology

Social Sciences

Social Sciences, Mathematical Methods

Details

Title: Subtitle: Efficiency in Pure-Exchange Economies With Risk-Averse Monetary Utilities
Creators: Mario Ghossoub - University of Waterloo
Michael B. Zhu - University of Hong Kong
Resource Type: Journal article
Publication Details: Mathematical finance, Vol.36(1), pp.99-117
DOI: 10.1111/mafi.70006
ISSN: 0960-1627
eISSN: 1467-9965
Publisher: Wiley
Number of pages: 19
Grant note: Society of Actuaries through the Hickman Scholars Program 2018-03961; 2024-03744 / Natural Sciences and Engineering Research Council of Canada (NSERC)
Language: English
Date published: 01/01/2026
Academic Unit: Statistics and Actuarial Science
Record Identifier: 9985179682902771

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