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Robust spectral risk optimization when information on risk spectrum Is incomplete

Robust spectral risk optimization when information on risk spectrum Is incomplete
Robust spectral risk optimization when information on risk spectrum Is incomplete
A spectral risk measure (SRM) is a weighted average of value at risk where the weighting function (also known as risk spectrum or distortion function) characterizes a decision maker's risk attitude. In this paper, we consider the case where the decision maker's risk spectrum is ambiguous and introduce a robust SRM model based on the worst risk spectrum from a ball of risk spectra centered at a nominal risk spectrum. When the ball consists of step-like risk spectra, we show that the robust SRM can be computed by solving a linear programming problem. For the general case, we propose a step-like approximation scheme and derive an error bound for the approximation. As an application, we apply the proposed robust SRM to one-stage stochastic optimization with the objective of minimizing the robust SRM and propose an alternating iterative algorithm for solving the resulting minimax optimization problem. Moreover, to examine stability of the robust spectral risk optimization model with respect to perturbation of observed data from the underlying exogenous uncertainty in data-driven environments, we investigate statistical robustness of the model and derive sufficient conditions for the required stability.
1052-6234
3198-3229
Wang, Wei
8b7c2f29-8ebf-4a6b-b7ab-a7287252886c
Xu, Huifu
d3200e0b-ad1d-4cf7-81aa-48f07fb1f8f5
Wang, Wei
8b7c2f29-8ebf-4a6b-b7ab-a7287252886c
Xu, Huifu
d3200e0b-ad1d-4cf7-81aa-48f07fb1f8f5

Wang, Wei and Xu, Huifu (2020) Robust spectral risk optimization when information on risk spectrum Is incomplete. SIAM Journal on Optimization, 30 (4), 3198-3229. (doi:10.1137/19M1284270).

Record type: Article

Abstract

A spectral risk measure (SRM) is a weighted average of value at risk where the weighting function (also known as risk spectrum or distortion function) characterizes a decision maker's risk attitude. In this paper, we consider the case where the decision maker's risk spectrum is ambiguous and introduce a robust SRM model based on the worst risk spectrum from a ball of risk spectra centered at a nominal risk spectrum. When the ball consists of step-like risk spectra, we show that the robust SRM can be computed by solving a linear programming problem. For the general case, we propose a step-like approximation scheme and derive an error bound for the approximation. As an application, we apply the proposed robust SRM to one-stage stochastic optimization with the objective of minimizing the robust SRM and propose an alternating iterative algorithm for solving the resulting minimax optimization problem. Moreover, to examine stability of the robust spectral risk optimization model with respect to perturbation of observed data from the underlying exogenous uncertainty in data-driven environments, we investigate statistical robustness of the model and derive sufficient conditions for the required stability.

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More information

Accepted/In Press date: 30 August 2020
e-pub ahead of print date: 24 November 2020

Identifiers

Local EPrints ID: 446873
URI: http://eprints.soton.ac.uk/id/eprint/446873
ISSN: 1052-6234
PURE UUID: 04548894-abc8-4aee-bef0-d6f7a03c9a29
ORCID for Huifu Xu: ORCID iD orcid.org/0000-0001-8307-2920

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Date deposited: 25 Feb 2021 17:30
Last modified: 29 Oct 2022 01:39

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Contributors

Author: Wei Wang
Author: Huifu Xu ORCID iD

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