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Multiple-Priors Optimal Investment In Discrete Time For Unbounded Utility Function

Author

Listed:
  • Romain Blanchard

    (LMR - Laboratoire de Mathématiques de Reims - URCA - Université de Reims Champagne-Ardenne - CNRS - Centre National de la Recherche Scientifique)

  • Laurence Carassus

    (Research Center - Léonard de Vinci Pôle Universitaire - De Vinci Research Center, URCA - Université de Reims Champagne-Ardenne)

Abstract

This paper investigates the problem of maximizing expected terminal utility in a discrete-time financial market model with a finite horizon under non-dominated model uncertainty. We use a dynamic programming framework together with measurable selection arguments to prove that under mild integrability conditions, an optimal portfolio exists for an unbounded utility function defined on the half-real line.

Suggested Citation

  • Romain Blanchard & Laurence Carassus, 2018. "Multiple-Priors Optimal Investment In Discrete Time For Unbounded Utility Function," Working Papers hal-01883787, HAL.
    • Handle: RePEc:hal:wpaper:hal-01883787
    Note: View the original document on HAL open archive server: https://hal.science/hal-01883787v1
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    Citations

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    Cited by:

    1. Miklós Rásonyi & Andrea Meireles‐Rodrigues, 2021. "On utility maximization under model uncertainty in discrete‐time markets," Mathematical Finance, Wiley Blackwell, vol. 31(1), pages 149-175, January.
    2. Areski Cousin & Ying Jiao & Christian y Robert & Olivier David Zerbib, 2021. "Optimal asset allocation subject to withdrawal risk and solvency constraints," Working Papers hal-03244380, HAL.
    3. Laurence Carassus & Emmanuel L'epinette, 2021. "Pricing without no-arbitrage condition in discrete time," Papers 2104.02688, arXiv.org.
    4. Laurence Carassus, 2021. "Quasi-sure essential supremum and applications to finance," Papers 2107.12862, arXiv.org, revised Mar 2024.
    5. Ariel Neufeld & Julian Sester & Mario Šikić, 2023. "Markov decision processes under model uncertainty," Mathematical Finance, Wiley Blackwell, vol. 33(3), pages 618-665, July.
    6. Daniel Bartl & Michael Kupper & Ariel Neufeld, 2021. "Duality theory for robust utility maximisation," Finance and Stochastics, Springer, vol. 25(3), pages 469-503, July.
    7. Huy N. Chau & Miklós Rásonyi, 2019. "Robust utility maximisation in markets with transaction costs," Finance and Stochastics, Springer, vol. 23(3), pages 677-696, July.
    8. Ariel Neufeld & Matthew Ng Cheng En & Ying Zhang, 2024. "Robust SGLD algorithm for solving non-convex distributionally robust optimisation problems," Papers 2403.09532, arXiv.org.
    9. Laurence Carassus & Johannes Wiesel, 2023. "Strategies with minimal norm are optimal for expected utility maximization under high model ambiguity," Papers 2306.01503, arXiv.org, revised Jan 2024.
    10. Shuoqing Deng & Xiaolu Tan & Xiang Yu, 2020. "Utility Maximization with Proportional Transaction Costs Under Model Uncertainty," Mathematics of Operations Research, INFORMS, vol. 45(4), pages 1210-1236, November.
    11. Laurence Carassus & Massinissa Ferhoune, 2024. "Nonconcave Robust Utility Maximization under Projective Determinacy," Papers 2403.11824, arXiv.org.
    12. Bartl, Daniel, 2020. "Conditional nonlinear expectations," Stochastic Processes and their Applications, Elsevier, vol. 130(2), pages 785-805.
    13. Ariel Neufeld & Julian Sester, 2024. "Non-concave distributionally robust stochastic control in a discrete time finite horizon setting," Papers 2404.05230, arXiv.org.
    14. David Criens & Lars Niemann, 2023. "Robust utility maximization with nonlinear continuous semimartingales," Mathematics and Financial Economics, Springer, volume 17, number 5, February.
    15. Ruslan Mirmominov & Johannes Wiesel, 2024. "A dynamic programming principle for multiperiod control problems with bicausal constraints," Papers 2410.23927, arXiv.org.
    16. Romain Blanchard & Laurence Carassus, 2019. "No-arbitrage with multiple-priors in discrete time," Papers 1904.08780, arXiv.org, revised Oct 2019.
    17. Laurence Carassus & Massinissa Ferhoune, 2023. "Discrete time optimal investment under model uncertainty," Papers 2307.11919, arXiv.org, revised Feb 2024.
    18. Areski Cousin & Ying Jiao & Christian Yann Robert & Olivier David Zerbib, 2022. "Optimal Asset Allocation Subject to Withdrawal Risk and Solvency Constraints," Risks, MDPI, vol. 10(1), pages 1-28, January.
    19. Blanchard, Romain & Carassus, Laurence, 2020. "No-arbitrage with multiple-priors in discrete time," Stochastic Processes and their Applications, Elsevier, vol. 130(11), pages 6657-6688.
    20. Daniel Bartl & Michael Kupper & Ariel Neufeld, 2020. "Duality Theory for Robust Utility Maximisation," Papers 2007.08376, arXiv.org, revised Jun 2021.
    21. Romain Blanchard & Laurence Carassus, 2021. "Convergence of utility indifference prices to the superreplication price in a multiple‐priors framework," Mathematical Finance, Wiley Blackwell, vol. 31(1), pages 366-398, January.

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