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Optimal investment with possibly non-concave utilities and no-arbitrage: a measure theoretical approach

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

    (PULV - Pôle Universitaire Léonard de Vinci)

  • Miklos Rasonyi

Abstract

We consider a discrete-time financial market model with finite time horizon and investors with utility functions d efined on the non-negative half-line. We allow these functions to be random, non-concave and non-smooth. We use a dynamic programming framework together with measurable selection arguments to establish both the characterization of the no-arbitrage property for such markets and the existence of an optimal portfolio strategy for such investors.

Suggested Citation

  • Romain Blanchard & Laurence Carassus & Miklos Rasonyi, 2018. "Optimal investment with possibly non-concave utilities and no-arbitrage: a measure theoretical approach," Post-Print hal-01883419, HAL.
    • Handle: RePEc:hal:journl:hal-01883419
    DOI: 10.1007/s00186-018-0635-3
    Note: View the original document on HAL open archive server: https://hal.science/hal-01883419
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    References listed on IDEAS

    as
    1. 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.
    2. Hanqing Jin & Xun Yu Zhou, 2008. "Behavioral Portfolio Selection In Continuous Time," Mathematical Finance, Wiley Blackwell, vol. 18(3), pages 385-426, July.
    3. repec:dau:papers:123456789/2317 is not listed on IDEAS
    4. Marcel Nutz, 2016. "Utility Maximization Under Model Uncertainty In Discrete Time," Mathematical Finance, Wiley Blackwell, vol. 26(2), pages 252-268, April.
    5. J. Jacod & A.N. Shiryaev, 1998. "Local martingales and the fundamental asset pricing theorems in the discrete-time case," Finance and Stochastics, Springer, vol. 2(3), pages 259-273.
    6. Miklos Rasonyi & Lukasz Stettner, 2005. "On utility maximization in discrete-time financial market models," Papers math/0505243, arXiv.org.
    7. Jörn Sass, 2005. "Portfolio optimization under transaction costs in the CRR model," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 61(2), pages 239-259, June.
    8. Alain Bensoussan & Abel Cadenillas & Hyeng Keun Koo, 2015. "Entrepreneurial Decisions on Effort and Project with a Nonconcave Objective Function," Mathematics of Operations Research, INFORMS, vol. 40(4), pages 902-914, October.
    9. 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.
    10. Charalambos D. Aliprantis & Kim C. Border, 2006. "Infinite Dimensional Analysis," Springer Books, Springer, edition 0, number 978-3-540-29587-7, December.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    no-arbitrage condition; non-concave utility functions; optimal investment;
    All these keywords.

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