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Distributionally Robust Optimization Under Moment Uncertainty with Application to Data-Driven Problems

Author

Listed:
  • Erick Delage

    (Department of Management Sciences, HEC Montréal, Montreal, Quebec H3T 2A7, Canada)

  • Yinyu Ye

    (Department of Management Science and Engineering, Stanford University, Stanford, California 94305)

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.

Suggested Citation

  • Erick Delage & Yinyu Ye, 2010. "Distributionally Robust Optimization Under Moment Uncertainty with Application to Data-Driven Problems," Operations Research, INFORMS, vol. 58(3), pages 595-612, June.
    • Handle: RePEc:inm:oropre:v:58:y:2010:i:3:p:595-612
    DOI: 10.1287/opre.1090.0741
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    References listed on IDEAS

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