Liu, Peng and Wang, Ruodu and Wei, Linxiao (2020) Is the inf-convolution of law-invariant preferences law-invariant? Insurance: Mathematics and Economics, 91. pp. 144-154. DOI https://doi.org/10.1016/j.insmatheco.2020.01.004
Liu, Peng and Wang, Ruodu and Wei, Linxiao (2020) Is the inf-convolution of law-invariant preferences law-invariant? Insurance: Mathematics and Economics, 91. pp. 144-154. DOI https://doi.org/10.1016/j.insmatheco.2020.01.004
Liu, Peng and Wang, Ruodu and Wei, Linxiao (2020) Is the inf-convolution of law-invariant preferences law-invariant? Insurance: Mathematics and Economics, 91. pp. 144-154. DOI https://doi.org/10.1016/j.insmatheco.2020.01.004
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 |
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Additional Information: | Rank-dependent utility |
Uncontrolled Keywords: | Law-invariance; Inf-convolution; Risk sharing; Cumulative prospect theory |
Divisions: | Faculty of Science and Health Faculty of Science and Health > Mathematics, Statistics and Actuarial Science, School of |
SWORD Depositor: | Unnamed user with email elements@essex.ac.uk |
Depositing User: | Unnamed user with email elements@essex.ac.uk |
Date Deposited: | 17 Aug 2020 20:48 |
Last Modified: | 30 Oct 2024 19:14 |
URI: | http://repository.essex.ac.uk/id/eprint/28165 |
Available files
Filename: infconvolution-1220.pdf
Licence: Creative Commons: Attribution-Noncommercial-No Derivative Works 3.0