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Is the inf-convolution of law-invariant preferences law-invariant?

Liu, Peng and Wang, Ruodu and Wei, Linxiao (2020) 'Is the inf-convolution of law-invariant preferences law-invariant?' Insurance: Mathematics and Economics, 91. 144 - 154. ISSN 0167-6687

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Abstract

We analyze the question of whether the inf-convolution of law-invariant risk functionals (preferences) is still law-invariant. In other words, we try to understand whether the representative economic agent (after risk redistribution) only cares about the distribution of the total risk, assuming all individual agents do so. Although the answer to the above question seems to be affirmative for many examples of commonly used risk functionals in the literature, the situation becomes delicate without assuming specific forms and properties of the individual functionals. We illustrate with examples the surprising fact that the answer to the main question is generally negative, even in an atomless probability space. Furthermore, we establish a few very weak conditions under which the answer becomes positive. These conditions do not require any specific forms or convexity of the risk functionals, and they are the richness of the underlying probability space, and monotonicity or continuity of one of the risk functionals. We provide several examples and counter-examples to discuss the subtlety of the question on law-invariance.

Item Type: Article
Additional Information: Rank-dependent utility
Uncontrolled Keywords: Law-invariance, Inf-convolution, Risk sharing, Cumulative prospect theory
Divisions: Faculty of Science and Health > Mathematical Sciences, Department of
Depositing User: Elements
Date Deposited: 17 Aug 2020 20:48
Last Modified: 05 Aug 2021 01:00
URI: http://repository.essex.ac.uk/id/eprint/28165

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