Robust multiobjective optimization & applications in portfolio optimization
Robust multiobjective optimization & applications in portfolio optimization
Motivated by Markowitz portfolio optimization problems under uncertainty in the problem data, we consider general convex parametric multiobjective optimization problems under data uncertainty. For the first time, this uncertainty is treated by a robust multiobjective formulation in the gist of Ben-Tal and Nemirovski. For this novel formulation, we investigate its relationship to the original multiobjective formulation as well as to its scalarizations. Further, we provide a characterization of the location of the robust Pareto frontier with respect to the corresponding original Pareto frontier and show that standard techniques from multiobjective optimization can be employed to characterize this robust efficient frontier. We illustrate our results based on a standard mean–variance problem.
robustification, uncertainty, markowitz, multiobjective
422-433
Fliege, Jörg
54978787-a271-4f70-8494-3c701c893d98
Werner, Ralf
056699b2-2ac9-4977-919e-da57a71f17cc
16 April 2014
Fliege, Jörg
54978787-a271-4f70-8494-3c701c893d98
Werner, Ralf
056699b2-2ac9-4977-919e-da57a71f17cc
Fliege, Jörg and Werner, Ralf
(2014)
Robust multiobjective optimization & applications in portfolio optimization.
[in special issue: 60 Years Following Harry Markowitz’s Contribution to Portfolio Theory and Operations Research]
European Journal of Operational Research, 234 (2), .
(doi:10.1016/j.ejor.2013.10.028).
Abstract
Motivated by Markowitz portfolio optimization problems under uncertainty in the problem data, we consider general convex parametric multiobjective optimization problems under data uncertainty. For the first time, this uncertainty is treated by a robust multiobjective formulation in the gist of Ben-Tal and Nemirovski. For this novel formulation, we investigate its relationship to the original multiobjective formulation as well as to its scalarizations. Further, we provide a characterization of the location of the robust Pareto frontier with respect to the corresponding original Pareto frontier and show that standard techniques from multiobjective optimization can be employed to characterize this robust efficient frontier. We illustrate our results based on a standard mean–variance problem.
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e-pub ahead of print date: 26 October 2013
Published date: 16 April 2014
Keywords:
robustification, uncertainty, markowitz, multiobjective
Organisations:
Operational Research
Identifiers
Local EPrints ID: 349778
URI: http://eprints.soton.ac.uk/id/eprint/349778
ISSN: 0377-2217
PURE UUID: 9c9cf47c-41aa-4513-9deb-88e6ebbc547a
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Date deposited: 16 Oct 2014 15:26
Last modified: 15 Mar 2024 03:30
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Author:
Ralf Werner
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