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No-arbitrage and optimal investment with possibly non-concave utilities: a measure theoretical approach

Author

Listed:
  • Romain Blanchard

    (Université Reims Champagne-Ardenne (URCA))

  • Laurence Carassus

    (Pôle Universitaire Léonard de Vinci
    Université Reims Champagne-Ardenne (URCA))

  • Miklós Rásonyi

    (MTA Alfréd Rényi Institute of Mathematics)

Abstract

We consider a discrete-time financial market model with finite time horizon and investors with utility functions defined 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 characterisation 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 & 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.
    • Handle: RePEc:spr:mathme:v:88:y:2018:i:2:d:10.1007_s00186-018-0635-3
    DOI: 10.1007/s00186-018-0635-3
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    References listed on IDEAS

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    9. 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.
    10. 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.
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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. Laurence Carassus & Massinissa Ferhoune, 2024. "Nonconcave Robust Utility Maximization under Projective Determinacy," Papers 2403.11824, arXiv.org.

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