A soft robust model for optimization under ambiguity
Abstract
In this paper, we propose a framework for robust optimization that relaxes the standard
notion of robustness by allowing the decision maker to vary the protection level in
a smooth way across the uncertainty set. We apply our approach to the problem of maximizing
the expected value of a payoff function when the underlying distribution is ambiguous
and therefore robustness is relevant. Our primary objective is to develop this framework
and relate it to the standard notion of robustness, which deals with only a single
guarantee across one uncertainty set. First, we show that our approach connects closely
to the theory of convex risk measures. We show that the complexity of this approach
is equivalent to that of solving a small number of standard robust problems. We then
investigate the conservatism benefits and downside probability guarantees implied
by this approach and compare to the standard robust approach. Finally, we illustrate
theme thodology on an asset allocation example consisting of historical market data
over a 25-year investment horizon and find in every case we explore that relaxing
standard robustness with soft robustness yields a seemingly favorable risk-return
trade-off: each case results in a higher out-of-sample expected return for a relatively
minor degradation of out-of-sample downside performance. © 2010 INFORMS.
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https://hdl.handle.net/10161/4438Published Version (Please cite this version)
10.1287/opre.1100.0821Publication Info
Ben-Tal, A; Bertsimas, D; & Brown, DB (2010). A soft robust model for optimization under ambiguity. Operations Research, 58(4 PART 2). pp. 1220-1234. 10.1287/opre.1100.0821. Retrieved from https://hdl.handle.net/10161/4438.This is constructed from limited available data and may be imprecise. To cite this
article, please review & use the official citation provided by the journal.
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Show full item recordScholars@Duke
David B. Brown
Professor of Business Administration
David B. Brown is a Professor at the Fuqua School of Business at Duke University.
He has been at Fuqua as a member of the Decision Sciences area since receiving his
Ph.D. in Electrical Engineering and Computer Science from MIT in 2006.
Professor Brown's research is within the field of operations research and focuses
broadly on the design and analysis of solution methods for large-scale optimization
problems involving uncertainty. This work entails the use of techniques from opti

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