Journal Article

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

Ye, Yinyu, Delage, Erick

2010

Overview

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.

• Publisher: INFORMS,Institute for Operations Research and the Management Sciences
• Subject: Applied sciences / Covariance matrices / Decision theory. Utility theory / Ellipsoids / estimation / Exact sciences and technology / finance / Hyperplanes / Mathematical functions / Mathematical inequalities / Mathematical moments / Mathematical programming / Mathematical vectors / Operational research and scientific management / Operational research. Management science / Optimal solutions / Optimization / Polynomials / portfolio / Portfolio management / Portfolio theory / programming / Robust optimization / statistics / stochastic / Stochastic models / Studies / Uncertainty