Distributionally robust stochastic programming. (English) Zbl 1373.90089
Summary: In this paper we study distributionally robust stochastic programming in a setting where there is a specified reference probability measure and the uncertainty set of probability measures consists of measures in some sense close to the reference measure. We discuss law invariance of the associated worst case functional and consider two basic constructions of such uncertainty sets. Finally we illustrate some implications of the property of law invariance.
MSC:
| 90C15 | Stochastic programming |
| 90C47 | Minimax problems in mathematical programming |
| 91B30 | Risk theory, insurance (MSC2010) |
Keywords:
coherent risk measures; law invariance; Wasserstein distance; \(\phi\)-divergence; sample average approximation; ambiguous chance constraintsReferences:
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