IDEAS home Printed from https://ideas.repec.org/p/arx/papers/1309.0362.html
   My bibliography  Save this paper

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/1309.0362
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. 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.
    2. 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.
    3. Hanqing Jin & Xun Yu Zhou, 2008. "Behavioral Portfolio Selection In Continuous Time," Mathematical Finance, Wiley Blackwell, vol. 18(3), pages 385-426, July.
    4. Daniel Kahneman & Amos Tversky, 2013. "Prospect Theory: An Analysis of Decision Under Risk," World Scientific Book Chapters, in: Leonard C MacLean & William T Ziemba (ed.), HANDBOOK OF THE FUNDAMENTALS OF FINANCIAL DECISION MAKING Part I, chapter 6, pages 99-127, World Scientific Publishing Co. Pte. Ltd..
    5. 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.
    6. Jakša Cvitanić & Ioannis Karatzas, 1996. "Hedging And Portfolio Optimization Under Transaction Costs: A Martingale Approach12," Mathematical Finance, Wiley Blackwell, vol. 6(2), pages 133-165, April.
    7. Kenneth J. Arrow, 1974. "The Use of Unbounded Utility Functions in Expected-Utility Maximization: Response," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 88(1), pages 136-138.
    8. Drazen Prelec, 1998. "The Probability Weighting Function," Econometrica, Econometric Society, vol. 66(3), pages 497-528, May.
    9. Roman Muraviev & L. Rogers, 2013. "Utilities bounded below," Annals of Finance, Springer, vol. 9(2), pages 271-289, May.
    10. Terence M. Ryan, 1974. "The Use of Unbounded Utility Functions in Expected-Utility Maximization: Comment," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 88(1), pages 133-135.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Miklos Rasonyi, 2014. "Optimal investment with bounded above utilities in discrete time markets," Papers 1409.2023, arXiv.org.
    2. 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.
    3. 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.
    4. Marcos Escobar-Anel & Michel Kschonnek & Rudi Zagst, 2022. "Portfolio optimization: not necessarily concave utility and constraints on wealth and allocation," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 95(1), pages 101-140, February.
    5. Jakusch, Sven Thorsten & Meyer, Steffen & Hackethal, Andreas, 2019. "Taming models of prospect theory in the wild? Estimation of Vlcek and Hens (2011)," SAFE Working Paper Series 146, Leibniz Institute for Financial Research SAFE, revised 2019.
    6. Stephen G Dimmock & Roy Kouwenberg & Olivia S Mitchell & Kim Peijnenburg, 2021. "Household Portfolio Underdiversification and Probability Weighting: Evidence from the Field," The Review of Financial Studies, Society for Financial Studies, vol. 34(9), pages 4524-4563.
    7. Zuo Quan Xu, 2014. "A Note on the Quantile Formulation," Papers 1403.7269, arXiv.org, revised Apr 2014.
    8. Bin Zou & Rudi Zagst, 2015. "Optimal Investment with Transaction Costs under Cumulative Prospect Theory in Discrete Time," Papers 1511.04768, arXiv.org, revised Nov 2016.
    9. Laurence Carassus & Miklós Rásonyi, 2016. "Maximization of Nonconcave Utility Functions in Discrete-Time Financial Market Models," Mathematics of Operations Research, INFORMS, vol. 41(1), pages 146-173, February.
    10. Marcos Escobar-Anel & Andreas Lichtenstern & Rudi Zagst, 2020. "Behavioral portfolio insurance strategies," Financial Markets and Portfolio Management, Springer;Swiss Society for Financial Market Research, vol. 34(4), pages 353-399, December.
    11. Zuo Quan Xu, 2018. "Pareto optimal moral-hazard-free insurance contracts in behavioral finance framework," Papers 1803.02546, arXiv.org, revised Aug 2021.
    12. 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.
    13. Bin Zou, 2017. "Optimal Investment In Hedge Funds Under Loss Aversion," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 20(03), pages 1-32, May.
    14. Massimiliano Amarante & Mario Ghossoub & Edmund Phelps, 2012. "Contracting for Innovation under Knightian Uncertainty," Cahiers de recherche 18-2012, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
    15. Alarie, Yves & Dionne, Georges, 2005. "Testing explanations of preference reversal: A model," Working Papers 05-2, HEC Montreal, Canada Research Chair in Risk Management.
    16. Mohammed Abdellaoui & Olivier L’Haridon & Horst Zank, 2010. "Separating curvature and elevation: A parametric probability weighting function," Journal of Risk and Uncertainty, Springer, vol. 41(1), pages 39-65, August.
    17. Foster, Gigi & Frijters, Paul & Schaffner, Markus & Torgler, Benno, 2018. "Expectation formation in an evolving game of uncertainty: New experimental evidence," Journal of Economic Behavior & Organization, Elsevier, vol. 154(C), pages 379-405.
    18. Che-Yuan Liang, 2017. "Optimal inequality behind the veil of ignorance," Theory and Decision, Springer, vol. 83(3), pages 431-455, October.
    19. Xue Dong He & Sang Hu & Jan Obłój & Xun Yu Zhou, 2017. "Technical Note—Path-Dependent and Randomized Strategies in Barberis’ Casino Gambling Model," Operations Research, INFORMS, vol. 65(1), pages 97-103, February.
    20. Kerim Keskin, 2016. "Inverse S-shaped probability weighting functions in first-price sealed-bid auctions," Review of Economic Design, Springer;Society for Economic Design, vol. 20(1), pages 57-67, March.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:arx:papers:1309.0362. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.