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Discrete time optimal investment under model uncertainty

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  • Carassus, Laurence
  • Ferhoune, Massinissa

Abstract

We study a robust utility maximisation problem in a general discrete-time frictionless market under quasi-sure no-arbitrage. The investor is assumed to have a random and concave utility function defined on the whole real line. She also faces model ambiguity in her beliefs about the market, which is modelled through a set of priors. We prove the existence of an optimal investment strategy using only primal methods. For that, we assume classical assumptions on the market and the random utility function as asymptotic elasticity constraints. Most of our other assumptions are stated on a prior-by-prior basis and correspond to generally accepted assumptions in the literature on markets without ambiguity. We also propose a general setting, including utility functions with benchmarks for which our assumptions can be easily checked.

Suggested Citation

  • Carassus, Laurence & Ferhoune, Massinissa, 2025. "Discrete time optimal investment under model uncertainty," Stochastic Processes and their Applications, Elsevier, vol. 189(C).
    • Handle: RePEc:eee:spapps:v:189:y:2025:i:c:s0304414925001498
    DOI: 10.1016/j.spa.2025.104708
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    References listed on IDEAS

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    1. Miklós Résonyi & Lukasz Stettner, 2006. "On the Existence of Optimal Portfolios for the Utility Maximization Problem in Discrete Time Financial Market Models," Springer Books, in: From Stochastic Calculus to Mathematical Finance, pages 589-608, Springer.
    2. Romain Blanchard & Laurence Carassus, 2019. "No-arbitrage with multiple-priors in discrete time," Papers 1904.08780, arXiv.org, revised Oct 2019.
    3. 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.
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    5. Mikl'os R'asonyi & Andrea Meireles-Rodrigues, 2018. "On Utility Maximisation Under Model Uncertainty in Discrete-Time Markets," Papers 1801.06860, arXiv.org, revised Jul 2020.
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    8. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
    9. Ariel Neufeld & Mario Sikic, 2017. "Nonconcave Robust Optimization with Discrete Strategies under Knightian Uncertainty," Papers 1711.03875, arXiv.org, revised Apr 2019.
    10. Romain Blanchard & Laurence Carassus, 2018. "Multiple-priors optimal investment in discrete time for unbounded utility function," Post-Print hal-01883787, HAL.
    11. Daniel Kahneman & Amos Tversky, 2013. "Prospect Theory: An Analysis of Decision Under Risk," World Scientific Book Chapters, in: Leonard C MacLean & William T Ziemba (ed.), HANDBOOK OF THE FUNDAMENTALS OF FINANCIAL DECISION MAKING Part I, chapter 6, pages 99-127, World Scientific Publishing Co. Pte. Ltd..
    12. repec:hal:wpaper:hal-01883787 is not listed on IDEAS
    13. Romain Blanchard & Laurence Carassus & Miklós Rásonyi, 2018. "No-arbitrage and optimal investment with possibly non-concave utilities: a measure theoretical approach," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 88(2), pages 241-281, October.
    14. 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.
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    Full references (including those not matched with items on IDEAS)

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