Distributionally Robust Optimization Under Moment Uncertainty with Application to Data-Driven Problems
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Abstract
Stochastic programming can effectively describe many decision-making problems in uncertain environments. Unfortunately, such programs are often computationally demanding to solve. In addition, their solution can be misleading when there is ambiguity in the choice of a distribution for the random parameters. In this paper, we propose a model that describes uncertainty in both the distribution form (discrete, Gaussian, exponential, etc.) and moments (mean and covariance matrix). We demonstrate that for a wide range of cost functions the associated distributionally robust (or min-max) stochastic program can be solved efficiently. Furthermore, by deriving a new confidence region for the mean and the covariance matrix of a random vector, we provide probabilistic arguments for using our model in problems that rely heavily on historical data. These arguments are confirmed in a practical example of portfolio selection, where our framework leads to better-performing policies on the “true” distribution underlying the daily returns of financial assets.
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The record
- Venue
- Operations Research
- Topic
- Risk and Portfolio Optimization
- Field
- Decision Sciences
- Canadian institutions
- HEC Montréal
- Funders
- —
- Keywords
- Mathematical optimizationComputer scienceProbabilistic logicAmbiguityPortfolio optimizationStochastic programmingPortfolioRobust optimizationCovarianceMoment (physics)Covariance matrixRange (aeronautics)Probability distributionGaussianOptimization problemMathematicsAlgorithmFinanceArtificial intelligenceStatistics
- Has abstract in OpenAlex
- yes