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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

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.

Suggested Citation

  • 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.
  • Handle: RePEc:arx:papers:1309.0362
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    References listed on IDEAS

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    1. Kahneman, Daniel & Tversky, Amos, 1979. "Prospect Theory: An Analysis of Decision under Risk," Econometrica, Econometric Society, vol. 47(2), pages 263-291, March.
    2. 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.
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    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. Kenneth J. Arrow, 1974. "The Use of Unbounded Utility Functions in Expected-Utility Maximization: Response," The Quarterly Journal of Economics, Oxford University Press, vol. 88(1), pages 136-138.
    7. Roman Muraviev & L. Rogers, 2013. "Utilities bounded below," Annals of Finance, Springer, vol. 9(2), pages 271-289, May.
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    9. Hanqing Jin & Xun Yu Zhou, 2008. "Behavioral Portfolio Selection In Continuous Time," Mathematical Finance, Wiley Blackwell, vol. 18(3), pages 385-426, July.
    10. 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.
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