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Non-concave optimal investment and no-arbitrage: a measure theoretical approach

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  • Romain Blanchard
  • Laurence Carassus
  • Mikl'os R'asonyi

Abstract

We consider non-concave and non-smooth random utility functions with do- main of definition equal to the non-negative half-line. We use a dynamic pro- gramming framework together with measurable selection arguments to establish both the no-arbitrage condition characterization and the existence of an optimal portfolio in a (generically incomplete) discrete-time financial market model with finite time horizon. In contrast to the existing literature, we propose to consider a probability space which is not necessarily complete.

Suggested Citation

  • Romain Blanchard & Laurence Carassus & Mikl'os R'asonyi, 2016. "Non-concave optimal investment and no-arbitrage: a measure theoretical approach," Papers 1602.06685, arXiv.org, revised Aug 2016.
    • Handle: RePEc:arx:papers:1602.06685
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    References listed on IDEAS

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    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. 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.
    5. Miklos Rasonyi & Lukasz Stettner, 2005. "On utility maximization in discrete-time financial market models," Papers math/0505243, arXiv.org.
    6. 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.
    7. Charalambos D. Aliprantis & Kim C. Border, 2006. "Infinite Dimensional Analysis," Springer Books, Springer, edition 0, number 978-3-540-29587-7, June.
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    Cited by:

    1. Romain Blanchard & Laurence Carassus, 2017. "Convergence of utility indifference prices to the superreplication price in a multiple-priors framework," Papers 1709.09465, arXiv.org, revised Oct 2020.

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