Preference robust distortion risk measure and its application
Preference robust distortion risk measure and its application
Distortion risk measure (DRM) plays a crucial role in management science and finance particularly actuarial science. Various DRMs have been introduced but little is discussed on which DRM at hand should be chosen to address a decision maker's (DM's) risk preference. This paper aims to fill out the gap. Specifically, we consider a situation where the true distortion function is unknown either because it is difficult to identify/elicit and/or because the DM's risk preference is ambiguous. We introduce a preference robust distortion risk measure (PRDRM), which is based on the worst-case distortion function from an ambiguity set of distortion functions to mitigate the impact arising from the ambiguity. The ambiguity set is constructed under well-known general principles such as concavity and inverse S-shapedness of distortion functions (overweighting on events from impossible to possible or possible to certainty and underweighting on those from possible to more possible) as well as new user-specific information such as sensitivity to tail losses, confidence intervals to some lotteries, and preferences to certain lotteries over others. To calculate the proposed PRDRM, we use the convex and/or concave envelope of a set of points to characterize the curvature of the distortion function and derive a tractable reformulation of the PRDRM when the underlying random loss is discretely distributed. Moreover, we show that the worst-case distortion function is a nondecreasing piecewise linear function and can be determined by solving a linear programming problem. Finally, we apply the proposed PRDRM to a risk capital allocation problem and carry out some numerical tests to examine the efficiency of the PRDRM model.
preference robust distortion risk measure, risk capital allocation, worst-case distortion function, Yaari's dual theory of choice
389-434
Wang, Wei
8b7c2f29-8ebf-4a6b-b7ab-a7287252886c
Xu, Huifu
d3200e0b-ad1d-4cf7-81aa-48f07fb1f8f5
April 2023
Wang, Wei
8b7c2f29-8ebf-4a6b-b7ab-a7287252886c
Xu, Huifu
d3200e0b-ad1d-4cf7-81aa-48f07fb1f8f5
Wang, Wei and Xu, Huifu
(2023)
Preference robust distortion risk measure and its application.
Mathematical Finance, 33 (2), .
(doi:10.1111/mafi.12379).
Abstract
Distortion risk measure (DRM) plays a crucial role in management science and finance particularly actuarial science. Various DRMs have been introduced but little is discussed on which DRM at hand should be chosen to address a decision maker's (DM's) risk preference. This paper aims to fill out the gap. Specifically, we consider a situation where the true distortion function is unknown either because it is difficult to identify/elicit and/or because the DM's risk preference is ambiguous. We introduce a preference robust distortion risk measure (PRDRM), which is based on the worst-case distortion function from an ambiguity set of distortion functions to mitigate the impact arising from the ambiguity. The ambiguity set is constructed under well-known general principles such as concavity and inverse S-shapedness of distortion functions (overweighting on events from impossible to possible or possible to certainty and underweighting on those from possible to more possible) as well as new user-specific information such as sensitivity to tail losses, confidence intervals to some lotteries, and preferences to certain lotteries over others. To calculate the proposed PRDRM, we use the convex and/or concave envelope of a set of points to characterize the curvature of the distortion function and derive a tractable reformulation of the PRDRM when the underlying random loss is discretely distributed. Moreover, we show that the worst-case distortion function is a nondecreasing piecewise linear function and can be determined by solving a linear programming problem. Finally, we apply the proposed PRDRM to a risk capital allocation problem and carry out some numerical tests to examine the efficiency of the PRDRM model.
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Mathematical Finance - 2023 - Wang - Preference robust distortion risk measure and its application
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Accepted/In Press date: 3 January 2023
e-pub ahead of print date: 26 February 2023
Published date: April 2023
Additional Information:
Funding Information:
We would like to thank the two anonymous referees for insightful comments and constructive suggestions, which help us strengthen the paper significantly. We would also like to thank the Associate Editor for the effective handling of the review. This work is supported by a CUHK direct grant.
Keywords:
preference robust distortion risk measure, risk capital allocation, worst-case distortion function, Yaari's dual theory of choice
Identifiers
Local EPrints ID: 476725
URI: http://eprints.soton.ac.uk/id/eprint/476725
ISSN: 0960-1627
PURE UUID: 7f268864-1ca4-4c5c-b330-2f89feeac2c9
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Date deposited: 12 May 2023 16:46
Last modified: 18 Mar 2024 02:57
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Author:
Wei Wang
Author:
Huifu Xu
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