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

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  • Miklos Rasonyi
  • Andrea M. Rodrigues
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    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.

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    File URL: http://arxiv.org/pdf/1202.0628
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    Bibliographic Info

    Paper provided by arXiv.org in its series Papers with number 1202.0628.

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    Date of creation: Feb 2012
    Date of revision: Apr 2013
    Handle: RePEc:arx:papers:1202.0628

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    Web page: http://arxiv.org/

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    1. 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.
    2. Bernard, Carole & Ghossoub, Mario, 2009. "Static Portfolio Choice under Cumulative Prospect Theory," MPRA Paper 15446, University Library of Munich, Germany.
    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. Berkelaar, A.B. & Kouwenberg, R.R.P., 2000. "Optimal portfolio choice under loss aversion," Econometric Institute Research Papers EI 2000-08/A, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    5. Hanqing Jin & Xun Yu Zhou, 2008. "Behavioral Portfolio Selection In Continuous Time," Mathematical Finance, Wiley Blackwell, vol. 18(3), pages 385-426.
    6. 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.
    7. Dana, Rose-Anne & Carlier, Guillaume, 2011. "Optimal Demand for Contingent Claims when Agents have law Invariant Utilities," Economics Papers from University Paris Dauphine 123456789/2317, Paris Dauphine University.
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    Cited by:
    1. 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.
    2. 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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