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Continuous-Time Portfolio Optimisation for a Behavioural Investor with Bounded Utility on Gains

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  • Mikl\'os R\'asonyi
  • Andrea Meireles Rodrigues
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    Abstract

    This paper examines an optimal investment problem in a continuous-time (essentially) complete financial market with a finite horizon. We deal with an investor who behaves consistently with principles of Cumulative Prospect Theory, and whose utility function on gains is bounded above. The well-posedness of the optimisation problem is trivial, and a necessary condition for the existence of an optimal trading strategy is derived. This condition requires that the investor's probability distortion function on losses does not tend to 0 near 0 faster than a given rate, which is determined by the utility function. Under additional assumptions, we show that this condition is indeed the borderline for attainability, in the sense that for slower convergence of the distortion function there does exist an optimal portfolio.

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    File URL: http://arxiv.org/pdf/1309.0362
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    Bibliographic Info

    Paper provided by arXiv.org in its series Papers with number 1309.0362.

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    Date of creation: Sep 2013
    Date of revision: Mar 2014
    Handle: RePEc:arx:papers:1309.0362

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    Web page: http://arxiv.org/

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    1. Ryan, Terence M, 1974. "The Use of Unbounded Utility Functions in Expected-Utility Maximization: Comment," The Quarterly Journal of Economics, MIT Press, vol. 88(1), pages 133-35, February.
    2. Hanqing Jin & Xun Yu Zhou, 2008. "Behavioral Portfolio Selection In Continuous Time," Mathematical Finance, Wiley Blackwell, vol. 18(3), pages 385-426.
    3. Drazen Prelec, 1998. "The Probability Weighting Function," Econometrica, Econometric Society, vol. 66(3), pages 497-528, May.
    4. 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.
    5. Amos Tversky & Daniel Kahneman, 1979. "Prospect Theory: An Analysis of Decision under Risk," Levine's Working Paper Archive 7656, David K. Levine.
    6. 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.
    7. Roman Muraviev & L. Rogers, 2013. "Utilities bounded below," Annals of Finance, Springer, vol. 9(2), pages 271-289, May.
    8. Jaksa Cvitanić & Ioannis Karatzas, 1996. "HEDGING AND PORTFOLIO OPTIMIZATION UNDER TRANSACTION COSTS: A MARTINGALE APPROACH-super-2," Mathematical Finance, Wiley Blackwell, vol. 6(2), pages 133-165.
    9. Miklós Rásonyi & Andrea Rodrigues, 2013. "Optimal portfolio choice for a behavioural investor in continuous-time markets," Annals of Finance, Springer, vol. 9(2), pages 291-318, May.
    10. Arrow, Kenneth J, 1974. "The Use of Unbounded Utility Functions in Expected-Utility Maximization: Response," The Quarterly Journal of Economics, MIT Press, vol. 88(1), pages 136-38, February.
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