Journal article
Counter-monotonic risk allocations and distortion risk measures
Scandinavian actuarial journal, Vol.2026(3), pp.324-347
03/16/2026
DOI: 10.1080/03461238.2025.2522201
Abstract
In risk-sharing markets with aggregate uncertainty, characterizing Pareto-optimal allocations when agents might not be risk averse is a challenging task, and the literature has only provided limited explicit results thus far. In particular, Pareto optima in such a setting may not necessarily be comonotonic, in contrast to the case of risk-averse agents. In fact, when market participants are risk-seeking, Pareto-optimal allocations are counter-monotonic. Counter-monotonicity of Pareto optima also arises in some situations for quantile-optimizing agents. In this paper, we provide a systematic study of efficient risk sharing in markets where allocations are constrained to be counter-monotonic. The preferences of the agents are modeled by a common distortion risk measure, or equivalently, by a common Yaari dual utility. We consider three different settings: risk-averse agents, risk-seeking agents, and those with an inverse S-shaped distortion function. In each case, we provide useful characterizations of optimal allocations, for both the counter-monotonic market and the unconstrained market. To illustrate our results, we consider an application to a portfolio choice problem for a portfolio manager tasked with managing the investments of a group of clients, with varying levels of risk aversion or risk seeking. We determine explicitly the optimal investment strategies in this case. Our results confirm the intuition that a manager investing on behalf of risk-seeking agents tends to invest more in risky assets than a manager acting on behalf of risk-averse agents.
Details
- Title: Subtitle
- Counter-monotonic risk allocations and distortion risk measures
- Creators
- Mario Ghossoub - University of WaterlooQinghua Ren - University of WaterlooRuodu Wang - University of Waterloo
- Resource Type
- Journal article
- Publication Details
- Scandinavian actuarial journal, Vol.2026(3), pp.324-347
- DOI
- 10.1080/03461238.2025.2522201
- ISSN
- 0346-1238
- eISSN
- 1651-2030
- Publisher
- Taylor & Francis
- Number of pages
- 24
- Grant note
- Natural Sciences and Engineering Research Council of Canada RGPIN-2024-03744; RGPIN-2024-03728; CRC-2022-00141 / Natural Sciences and Engineering Research Council of Canada
- Language
- English
- Date published
- 03/16/2026
- Academic Unit
- Statistics and Actuarial Science
- Record Identifier
- 9985179680002771
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