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On Utility Maximisation Under Model Uncertainty in Discrete-Time Markets

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  • Mikl'os R'asonyi
  • Andrea Meireles-Rodrigues

Abstract

We study the problem of maximising terminal utility for an agent facing model uncertainty, in a frictionless discrete-time market with one safe asset and finitely many risky assets. We show that an optimal investment strategy exists if the utility function, defined either over the positive real line or over the whole real line, is bounded from above. We further find that the boundedness assumption can be dropped provided that we impose suitable integrability conditions, related to some strengthened form of no-arbitrage. These results are obtained in an alternative framework for model uncertainty, where all possible dynamics of the stock prices are represented by a collection of stochastic processes on the same filtered probability space, rather than by a family of probability measures.

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  • 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.
    • Handle: RePEc:arx:papers:1801.06860
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    References listed on IDEAS

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    1. Schachermayer, W., 1992. "A Hilbert space proof of the fundamental theorem of asset pricing in finite discrete time," Insurance: Mathematics and Economics, Elsevier, vol. 11(4), pages 249-257, December.
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    3. Marcel Nutz, 2016. "Utility Maximization Under Model Uncertainty In Discrete Time," Mathematical Finance, Wiley Blackwell, vol. 26(2), pages 252-268, April.
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    6. Alexander Schied, 2005. "Optimal Investments for Robust Utility Functionals in Complete Market Models," Mathematics of Operations Research, INFORMS, vol. 30(3), pages 750-764, August.
    7. Miklos Rasonyi & Lukasz Stettner, 2005. "On utility maximization in discrete-time financial market models," Papers math/0505243, arXiv.org.
    8. Daniel Bartl, 2016. "Exponential utility maximization under model uncertainty for unbounded endowments," Papers 1610.00999, arXiv.org, revised Feb 2019.
    9. Miklos Rasonyi & Andrea M. Rodrigues, 2012. "Optimal Portfolio Choice for a Behavioural Investor in Continuous-Time Markets," Papers 1202.0628, arXiv.org, revised Apr 2013.
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    Cited by:

    1. Romain Blanchard & Laurence Carassus, 2019. "No-arbitrage with multiple-priors in discrete time," Papers 1904.08780, arXiv.org, revised Oct 2019.
    2. Laurence Carassus & Massinissa Ferhoune, 2023. "Discrete time optimal investment under model uncertainty," Papers 2307.11919, arXiv.org, revised Feb 2024.
    3. Huy N. Chau & Miklos Rasonyi, 2018. "Robust utility maximization in markets with transaction costs," Papers 1803.04213, arXiv.org, revised Dec 2018.
    4. Huy N. Chau & Masaaki Fukasawa & Miklos Rasonyi, 2021. "Super-replication with transaction costs under model uncertainty for continuous processes," Papers 2102.02298, arXiv.org.
    5. Laurence Carassus & Massinissa Ferhoune, 2024. "Nonconcave Robust Utility Maximization under Projective Determinacy," Papers 2403.11824, arXiv.org.

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