IDEAS home Printed from https://ideas.repec.org/a/bla/mathfi/v16y2006i2p283-299.html
   My bibliography  Save this article

Portfolio Optimization With Downside Constraints

Author

Listed:
  • Peter Lakner
  • Lan Ma Nygren

Abstract

We consider the portfolio optimization problem for an investor whose consumption rate process and terminal wealth are subject to downside constraints. In the standard financial market model that consists of d risky assets and one riskless asset, we assume that the riskless asset earns a constant instantaneous rate of interest, r > 0, and that the risky assets are geometric Brownian motions. The optimal portfolio policy for a wide scale of utility functions is derived explicitly. The gradient operator and the Clark–Ocone formula in Malliavin calculus are used in the derivation of this policy. We show how Malliavin calculus approach can help us get around certain difficulties that arise in using the classical “delta hedging” approach.

Suggested Citation

  • Peter Lakner & Lan Ma Nygren, 2006. "Portfolio Optimization With Downside Constraints," Mathematical Finance, Wiley Blackwell, vol. 16(2), pages 283-299, April.
    • Handle: RePEc:bla:mathfi:v:16:y:2006:i:2:p:283-299
    DOI: 10.1111/j.1467-9965.2006.00272.x
    as

    Download full text from publisher

    File URL: https://doi.org/10.1111/j.1467-9965.2006.00272.x
    Download Restriction: no
    File URL: https://libkey.io/10.1111/j.1467-9965.2006.00272.x?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Song, Jingjing & Bi, Xiuchun & Li, Rong & Zhang, Shuguang, 2017. "Optimal consumption and portfolio selection problems under loss aversion with downside consumption constraints," Applied Mathematics and Computation, Elsevier, vol. 299(C), pages 80-94.
    2. Kamma, Thijs & Pelsser, Antoon, 2022. "Near-optimal asset allocation in financial markets with trading constraints," European Journal of Operational Research, Elsevier, vol. 297(2), pages 766-781.
    3. Yuan, Haili & Hu, Yijun, 2009. "Optimal consumption and portfolio policies with the consumption habit constraints and the terminal wealth downside constraints," Insurance: Mathematics and Economics, Elsevier, vol. 45(3), pages 405-409, December.
    4. Wei-Ting Pan, 2016. "The Impact of Mandatory Savings on Life Cycle Consumption and Portfolio Choice," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 32, July-Dece.
    5. Kraft, Holger & Steffensen, Mogens, 2012. "A dynamic programming approach to constrained portfolios," CFS Working Paper Series 2012/07, Center for Financial Studies (CFS).
    6. Morten Tolver Kronborg, 2014. "Optimal Consumption and Investment with Labor Income and European/American Capital Guarantee," Risks, MDPI, vol. 2(2), pages 1-24, May.
    7. Thijs Kamma & Antoon Pelsser, 2019. "Near-Optimal Dynamic Asset Allocation in Financial Markets with Trading Constraints," Papers 1906.12317, arXiv.org, revised Oct 2019.
    8. Frank Seifried, 2010. "Optimal investment with deferred capital gains taxes," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 71(1), pages 181-199, February.
    9. Thomas Breuer & Martin Jandačka, 2008. "Portfolio selection with transaction costs under expected shortfall constraints," Computational Management Science, Springer, vol. 5(4), pages 305-316, October.
    10. Jörn Sass & Ralf Wunderlich, 2010. "Optimal portfolio policies under bounded expected loss and partial information," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 72(1), pages 25-61, August.
    11. Kraft, Holger & Steffensen, Mogens, 2013. "A dynamic programming approach to constrained portfolios," European Journal of Operational Research, Elsevier, vol. 229(2), pages 453-461.
    12. Feghhi Kashani , Mohammad & Mohebimajd , Ahmadreza, 2021. "Outperformance Testing of a Dynamic Assets Portfolio Selection Supplemented with a Continuous Paths Levy Process," Journal of Money and Economy, Monetary and Banking Research Institute, Central Bank of the Islamic Republic of Iran, vol. 16(2), pages 253-282, June.
    13. Jacobovic, Royi & Kella, Offer, 2020. "Minimizing a stochastic convex function subject to stochastic constraints and some applications," Stochastic Processes and their Applications, Elsevier, vol. 130(11), pages 7004-7018.
    14. Marcos Escobar-Anel, 2022. "A dynamic programming approach to path-dependent constrained portfolios," Annals of Operations Research, Springer, vol. 315(1), pages 141-157, August.
    15. Kristoffer Lindensjo, 2016. "An explicit formula for optimal portfolios in complete Wiener driven markets: a functional It\^o calculus approach," Papers 1610.05018, arXiv.org, revised Dec 2017.
    16. Bai, Zhidong & Liu, Huixia & Wong, Wing-Keung, 2016. "Making Markowitz's Portfolio Optimization Theory Practically Useful," MPRA Paper 74360, University Library of Munich, Germany.
    17. Steffensen, Mogens, 2011. "Optimal consumption and investment under time-varying relative risk aversion," Journal of Economic Dynamics and Control, Elsevier, vol. 35(5), pages 659-667, May.
    18. Lim, Byung Hwa & Lee, Ho-Seok & Shin, Yong Hyun, 2018. "The effects of pre-/post-retirement downside consumption constraints on optimal consumption, portfolio, and retirement," Finance Research Letters, Elsevier, vol. 25(C), pages 213-221.
    19. Andreas Lichtenstern & Pavel V. Shevchenko & Rudi Zagst, 2019. "Optimal life-cycle consumption and investment decisions under age-dependent risk preferences," Papers 1908.09976, arXiv.org.
    20. Wei-Ting Pan, 2016. "The Impact of Mandatory Savings on Life Cycle Consumption and Portfolio Choice," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 2-2016.

    More about this item

    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:bla:mathfi:v:16:y:2006:i:2:p:283-299. 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.

    We have no bibliographic references for this item. You can help adding them by using 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: Wiley Content Delivery (email available below). General contact details of provider: http://www.blackwellpublishing.com/journal.asp?ref=0960-1627 .

    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.