A framework for optimization under ambiguity

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Abstract

In this paper, single stage stochastic programs with ambiguous distributions for the involved random variables are considered. Though the true distribution is unknown, existence of a reference measure P̂ enables the construction of non-parametric ambiguity sets as Kantorovich balls around P̂. The original stochastic optimization problems are robustified by a worst case approach with respect to these ambiguity sets. The resulting problems are infinite optimization problems and can therefore not be solved computationally by straightforward methods. To nevertheless solve the robustified problems numerically, equivalent formulations as finite dimensional non-convex, semi definite saddle point problems are proposed. Finally an application from portfolio selection is studied for which methods to solve the robust counterpart problems explicitly are proposed and numerical results for sample problems are computed.

Original languageEnglish
Pages (from-to)21-47
Number of pages27
JournalAnnals of Operations Research
Volume193
Issue number1
DOIs
StatePublished - Mar 2012
Externally publishedYes

Keywords

  • Difference of convex algorithm
  • Expected shortfall
  • Non-convex optimization
  • Portfolio management
  • Robust optimization
  • Semi definite programming

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