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Nonconcave Robust Optimization with Discrete Strategies under Knightian Uncertainty


  • Ariel Neufeld
  • Mario Sikic


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.

Suggested Citation

  • Ariel Neufeld & Mario Sikic, 2017. "Nonconcave Robust Optimization with Discrete Strategies under Knightian Uncertainty," Papers 1711.03875,, revised Apr 2019.
  • Handle: RePEc:arx:papers:1711.03875

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    References listed on IDEAS

    1. Marcel Nutz & Jianfeng Zhang, 2012. "Optimal stopping under adverse nonlinear expectation and related games," Papers 1212.2140,, revised Sep 2015.
    2. Anis Matoussi & Dylan Possamaï & Chao Zhou, 2015. "Robust Utility Maximization In Nondominated Models With 2bsde: The Uncertain Volatility Model," Mathematical Finance, Wiley Blackwell, vol. 25(2), pages 258-287, April.
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    7. Christian Reichlin, 2016. "Behavioral Portfolio Selection: Asymptotics And Stability Along A Sequence Of Models," Mathematical Finance, Wiley Blackwell, vol. 26(1), pages 51-85, January.
    8. Bayraktar, Erhan & Yao, Song, 2011. "Optimal stopping for non-linear expectations--Part I," Stochastic Processes and their Applications, Elsevier, vol. 121(2), pages 185-211, February.
    9. Bruno Bouchard & Marcel Nutz, 2013. "Arbitrage and duality in nondominated discrete-time models," Papers 1305.6008,, revised Mar 2015.
    10. Sara Biagini & Mustafa Pinar, 2015. "The Robust Merton Problem of an Ambiguity Averse Investor," Papers 1502.02847,
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    12. Lin, Qian & Riedel, Frank, 2014. "Optimal consumption and portfolio choice with ambiguity," Center for Mathematical Economics Working Papers 497, Center for Mathematical Economics, Bielefeld University.
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