Stability and sensitivity of stochastic dominance constrained optimization models

Darinka Dentcheva, Werner Römisch

Research output: Contribution to journalArticlepeer-review

16 Scopus citations

Abstract

We consider convex optimization problems with kth order stochastic dominance constraints for κ ≥ 2. We discuss distances of random variables that are relevant for the dominance relation and establish quantitative stability results for optimal values and solution sets of the optimization problems in terms of a suitably selected probability metrics. Moreover, we provide conditions ensuring Hadamard directional differentiablity of the optimal value function. We introduce the notion of a shadow utility, which determines the changes of the optimal value when the underlying random variables are perturbed. Finally, we derive a limit theorem for the optimal values of empirical (Monte Carlo, sample average) approximations of dominance constrained optimization models.

Original languageEnglish
Pages (from-to)1672-1688
Number of pages17
JournalSIAM Journal on Optimization
Volume23
Issue number3
DOIs
StatePublished - 2013

Keywords

  • Empirical approximation
  • Higher order stochastic dominance
  • Risk
  • Shadow utility
  • Stochastic order

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