Imperial College London
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ProfessorEdwardAnderson

Business School

Professor of Analytics and Operations Management
 
 
 
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Contact

 

e.anderson

 
 
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Location

 

392Business School BuildingSouth Kensington Campus

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Summary

 

Publications

Citation

BibTex format

@article{Anderson:2020:10.1007/s10107-018-01359-8,
author = {Anderson, E and Xu, H and Zhang, D},
doi = {10.1007/s10107-018-01359-8},
journal = {Mathematical Programming},
pages = {327--370},
title = {Varying confidence levels for CVaR risk measures and minimax limits},
url = {http://dx.doi.org/10.1007/s10107-018-01359-8},
volume = {180},
year = {2020}
}
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RIS format (EndNote, RefMan)

TY  - JOUR
AB  - Conditional value at risk (CVaR) has been widely studied as a risk measure. In this paper we add to this work by focusing on the choice of confidence level and its impact on optimization problems with CVaR appearing in the objective and also the constraints. We start by considering a problem in which CVaR is minimized and investigate the way in which it approximates the minimax robust optimization problem as the confidence level is driven to one. We make use of a consistent tail condition which ensures that the CVaR of a random function will converge uniformly to its supremum as the confidence level increases, and establish an error bound for the CVaR optimal solution under second order growth conditions. The results are extended to a minimization problem with a constraint on the CVaR value which in the limit as the confidence level approaches one coincides with a problem having semi-infinite constraints. We study the sample average approximation scheme for the CVaR constraints and establish an exponential rate of convergence for the sample averaged optimal solution. We propose a procedure to explore the possibility of varying the confidence level to a lower value which can give an advantage when there is a need to find good solutions to CVaR-constrained problems out of sample. Our numerical results demonstrate that using the optimal solution to an adjusted problem with lower confidence level can lead to better overall performance.
AU  - Anderson,E
AU  - Xu,H
AU  - Zhang,D
DO  - 10.1007/s10107-018-01359-8
EP  - 370
PY  - 2020///
SN  - 0025-5610
SP  - 327
TI  - Varying confidence levels for CVaR risk measures and minimax limits
T2  - Mathematical Programming
UR  - http://dx.doi.org/10.1007/s10107-018-01359-8
UR  - https://link.springer.com/article/10.1007%2Fs10107-018-01359-8
UR  - http://hdl.handle.net/10044/1/79153
VL  - 180
ER  -
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