Robust Mean-Covariance Solutions for Stochastic Optimization

Ioana Popescu ()
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Ioana Popescu: Decision Sciences Area, INSEAD, Boulevard de Constance, 77300 Fontainebleau, France

Operations Research, 2007, vol. 55, issue 1, 98-112

Abstract: We provide a method for deriving robust solutions to certain stochastic optimization problems, based on mean-covariance information about the distributions underlying the uncertain vector of returns. We prove that for a general class of objective functions, the robust solutions amount to solving a certain deterministic parametric quadratic program. We first prove a general projection property for multivariate distributions with given means and covariances, which reduces our problem to optimizing a univariate mean-variance robust objective. This allows us to use known univariate results in the multidimensional setting, and to add new results in this direction. In particular, we characterize a general class of objective functions (the so-called one- or two-point support functions), for which the robust objective is reduced to a deterministic optimization problem in one variable. Finally, we adapt a result from Geoffrion (1967a) to reduce the main problem to a parametric quadratic program. In particular, our results are true for increasing concave utilities with convex or concave-convex derivatives. Closed-form solutions are obtained for special discontinuous criteria, motivated by bonus- and commission-based incentive schemes for portfolio management. We also investigate a multiproduct pricing application, which motivates extensions of our results for the case of nonnegative and decision-dependent returns.

Keywords: programming; stochastic; quadratic; decision analysis; risk; finance; portfolio (search for similar items in EconPapers)
Date: 2007
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Citations: View citations in EconPapers (51)

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Persistent link: https://EconPapers.repec.org/RePEc:inm:oropre:v:55:y:2007:i:1:p:98-112

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