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Optimal Portfolio Choice for a Behavioural Investor in Continuous-Time Markets

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  • Miklos Rasonyi
  • Andrea M. Rodrigues

Abstract

The aim of this work consists in the study of the optimal investment strategy for a behavioural investor, whose preference towards risk is described by both a probability distortion and an S-shaped utility function. Within a continuous-time financial market framework and assuming that asset prices are modelled by semimartingales, we derive sufficient and necessary conditions for the well-posedness of the optimisation problem in the case of piecewise-power probability distortion and utility functions. Finally, under straightforwardly verifiable conditions, we further demonstrate the existence of an optimal strategy.

Suggested Citation

  • 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.
  • Handle: RePEc:arx:papers:1202.0628
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    File URL: http://arxiv.org/pdf/1202.0628
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    References listed on IDEAS

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    1. Robert Kast & André Lapied & Pascal Toquebeuf, 2008. "Updating Choquet Integrals , Consequentialism and Dynamic Consistency," ICER Working Papers - Applied Mathematics Series 04-2008, ICER - International Centre for Economic Research.
    2. Arjan B. Berkelaar & Roy Kouwenberg & Thierry Post, 2004. "Optimal Portfolio Choice under Loss Aversion," The Review of Economics and Statistics, MIT Press, vol. 86(4), pages 973-987, November.
    3. Xue Dong He & Xun Yu Zhou, 2011. "Portfolio Choice Under Cumulative Prospect Theory: An Analytical Treatment," Management Science, INFORMS, vol. 57(2), pages 315-331, February.
    4. Hanqing Jin & Xun Yu Zhou, 2008. "Behavioral Portfolio Selection In Continuous Time," Mathematical Finance, Wiley Blackwell, vol. 18(3), pages 385-426.
    5. Tversky, Amos & Kahneman, Daniel, 1992. "Advances in Prospect Theory: Cumulative Representation of Uncertainty," Journal of Risk and Uncertainty, Springer, vol. 5(4), pages 297-323, October.
    6. Bernard, Carole & Ghossoub, Mario, 2009. "Static Portfolio Choice under Cumulative Prospect Theory," MPRA Paper 15446, University Library of Munich, Germany.
    7. repec:dau:papers:123456789/2317 is not listed on IDEAS
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    Cited by:

    1. Huy N. Chau & Mikl'os R'asonyi, 2016. "Skorohod's representation theorem and optimal strategies for markets with frictions," Papers 1606.07311, arXiv.org, revised Apr 2017.
    2. Mikl'os R'asonyi & Jos'e Gregorio Rodr'iguez-Villarreal, 2015. "Optimal investment under behavioural criteria in incomplete diffusion market models," Papers 1501.01504, arXiv.org.
    3. Mikl'os R'asonyi & Andrea Meireles Rodrigues, 2013. "Continuous-Time Portfolio Optimisation for a Behavioural Investor with Bounded Utility on Gains," Papers 1309.0362, arXiv.org, revised Mar 2014.
    4. Mikl'os R'asonyi & Andrea Meireles-Rodrigues, 2018. "On Utility Maximisation Under Model Uncertainty in Discrete-Time Markets," Papers 1801.06860, arXiv.org, revised Feb 2018.
    5. Miklos Rasonyi, 2014. "Optimal investment with bounded above utilities in discrete time markets," Papers 1409.2023, arXiv.org.
    6. Mikl'os R'asonyi & Jos'e G. Rodr'iguez-Villarreal, 2014. "Optimal investment under behavioural criteria -- a dual approach," Papers 1405.3812, arXiv.org, revised Jun 2014.

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