Nonconcave robust optimization with discrete strategies under Knightian uncertainty

Abstract

We study robust stochastic optimization problems in the quasi-sure setting in discrete-time. The strategies in the multi-period-case are restricted to those taking values in a discrete set. The optimization problems under consideration are not concave. We provide conditions under which a maximizer exists. The class of problems covered by our robust optimization problem includes optimal stopping and semi-static trading under Knightian uncertainty.

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Correspondence to Ariel Neufeld.

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Ariel Neufeld: Financial support by the NAP Grant as well as ETH RiskLab and the Swiss National Foundation Grant SNF 200020_172815 is gratefully acknowledged.

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Neufeld, A., Šikić, M. Nonconcave robust optimization with discrete strategies under Knightian uncertainty. Math Meth Oper Res 90, 229–253 (2019). https://doi.org/10.1007/s00186-019-00669-7

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Keywords

  • Nonconcave robust optimization
  • Robust utility maximization
  • Knightian uncertainty

Mathematics Subject Classification

  • 93E20
  • 49L20
  • 91B16