Portfolio optimization with pw-robustness

Virginie Gabrel (), Cécile Murat () and Aurélie Thiele ()
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Virginie Gabrel: Université Paris-Dauphine, PSL Research University, CNRS, LAMSADE
Cécile Murat: Université Paris-Dauphine, PSL Research University, CNRS, LAMSADE
Aurélie Thiele: Southern Methodist University

EURO Journal on Computational Optimization, 2018, vol. 6, issue 3, No 4, 267-290

Abstract: Abstract This paper investigates a portfolio optimization problem under uncertainty on the stock returns, where the manager seeks to achieve an appropriate trade-off between the expected portfolio return and the risk of loss. The uncertainty set consists of a finite set of scenarios occurring with equal probability. We introduce a new robustness criterion, called pw-robustness, which seeks to maximize the portfolio return in a proportion p of scenarios and guarantees a minimum return over all scenarios. We model this optimization problem as a mixed-integer programming problem. Through extensive numerical experiments, we identify the instances that can be solved to optimality in an acceptable time using off-the-shelf software. For the instances that cannot be solved to optimality within the time frame, we propose and test a heuristic that exhibits excellent practical performance in terms of computation time and solution quality for the problems we consider. This new criterion and our heuristic methods therefore exhibit great promise to tackle robustness problems when the uncertainty set consists of a large number of scenarios.

Keywords: Portfolio optimization; Robust optimization; Value-at-risk; 90C90 (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (4)

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DOI: 10.1007/s13675-018-0096-8

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