Computing bounds for stochastic programming problems by means of a generalized moment problem
Mathematics of Operations Research
A class of utility functions containing all the common utility functions
Management Science
One-switch utility functions and a measure of risk
Management Science
Bounding separable recourse functions with limited distribution information
Annals of Operations Research
A Tchebysheff-type bound on the expectation of sublinear polyhedral functions
Operations Research
Robust portfolio selection problems
Mathematics of Operations Research
IEEE Transactions on Information Theory
Theory and Applications of Robust Optimization
SIAM Review
A Distributional Interpretation of Robust Optimization
Mathematics of Operations Research
On the correlations between fuzzy variables
ICSI'10 Proceedings of the First international conference on Advances in Swarm Intelligence - Volume Part II
Game Theoretical Approach for Reliable Enhanced Indexation
Decision Analysis
Distributionally Robust Markov Decision Processes
Mathematics of Operations Research
Price of Correlations in Stochastic Optimization
Operations Research
Journal of Computational and Applied Mathematics
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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.