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Nonconcave robust optimization with discrete strategies under Knightian uncertainty

Author

Listed:
  • Ariel Neufeld

    (Nanyang Technological University)

  • Mario Šikić

    (University of Zurich)

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.

Suggested Citation

  • Ariel Neufeld & Mario Šikić, 2019. "Nonconcave robust optimization with discrete strategies under Knightian uncertainty," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 90(2), pages 229-253, October.
    • Handle: RePEc:spr:mathme:v:90:y:2019:i:2:d:10.1007_s00186-019-00669-7
    DOI: 10.1007/s00186-019-00669-7
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    References listed on IDEAS

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    1. Marcel Nutz & Jianfeng Zhang, 2012. "Optimal stopping under adverse nonlinear expectation and related games," Papers 1212.2140, arXiv.org, 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.
    3. I. V. Evstigneev, 1976. "Measurable Selection and Dynamic Programming," Mathematics of Operations Research, INFORMS, vol. 1(3), pages 267-272, August.
    4. Marcel Nutz, 2016. "Utility Maximization Under Model Uncertainty In Discrete Time," Mathematical Finance, Wiley Blackwell, vol. 26(2), pages 252-268, April.
    5. Revaz Tevzadze & Teimuraz Toronjadze & Tamaz Uzunashvili, 2013. "Robust utility maximization for a diffusion market model with misspecified coefficients," Finance and Stochastics, Springer, vol. 17(3), pages 535-563, July.
    6. Ariel Neufeld & Mario Sikic, 2016. "Robust Utility Maximization in Discrete-Time Markets with Friction," Papers 1610.09230, arXiv.org, revised May 2018.
    7. Alexandre Roch & H. Mete Soner, 2013. "Resilient Price Impact Of Trading And The Cost Of Illiquidity," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 16(06), pages 1-27.
    8. 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.
    9. Bruno Bouchard & Marcel Nutz, 2013. "Arbitrage and duality in nondominated discrete-time models," Papers 1305.6008, arXiv.org, revised Mar 2015.
    10. Daniel Bartl, 2016. "Exponential utility maximization under model uncertainty for unbounded endowments," Papers 1610.00999, arXiv.org, revised Feb 2019.
    11. Laurence Carassus & Mikl'os R'asonyi & Andrea M. Rodrigues, 2015. "Non-concave utility maximisation on the positive real axis in discrete time," Papers 1501.03123, arXiv.org, revised Apr 2015.
    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.
    13. Laurence Carassus & Miklós Rásonyi, 2016. "Maximization of Nonconcave Utility Functions in Discrete-Time Financial Market Models," Mathematics of Operations Research, INFORMS, vol. 41(1), pages 146-173, February.
    14. Halil Mete Soner & Mirjana Vukelja, 2013. "Utility Maximization in an Illiquid Market," Swiss Finance Institute Research Paper Series 13-17, Swiss Finance Institute.
    15. Ariel Neufeld & Marcel Nutz, 2018. "Robust Utility Maximization With Lã‰Vy Processes," Mathematical Finance, Wiley Blackwell, vol. 28(1), pages 82-105, January.
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    Cited by:

    1. Laurence Carassus & Massinissa Ferhoune, 2023. "Discrete time optimal investment under model uncertainty," Papers 2307.11919, arXiv.org, revised Feb 2024.
    2. Ariel Neufeld & Julian Sester & Mario Šikić, 2023. "Markov decision processes under model uncertainty," Mathematical Finance, Wiley Blackwell, vol. 33(3), pages 618-665, July.
    3. Daniel Bartl & Michael Kupper & Ariel Neufeld, 2021. "Duality theory for robust utility maximisation," Finance and Stochastics, Springer, vol. 25(3), pages 469-503, July.
    4. Daniel Bartl & Michael Kupper & Ariel Neufeld, 2020. "Duality Theory for Robust Utility Maximisation," Papers 2007.08376, arXiv.org, revised Jun 2021.
    5. Jonas Blessing & Michael Kupper & Alessandro Sgarabottolo, 2024. "Discrete approximation of risk-based prices under volatility uncertainty," Papers 2411.00713, arXiv.org.
    6. Laurence Carassus & Massinissa Ferhoune, 2024. "Nonconcave Robust Utility Maximization under Projective Determinacy," Papers 2403.11824, arXiv.org.
    7. Ariel Neufeld & Julian Sester, 2024. "Non-concave distributionally robust stochastic control in a discrete time finite horizon setting," Papers 2404.05230, arXiv.org.

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