IDEAS home Printed from https://ideas.repec.org/a/bla/mathfi/v16y2006i1p203-216.html
   My bibliography  Save this article

Markowitz'S Portfolio Optimization In An Incomplete Market

Author

Listed:
  • Jianming Xia
  • Jia‐An Yan

Abstract

In this paper, for a process S, we establish a duality relation between Kp, the ‐ closure of the space of claims in , which are attainable by “simple” strategies, and , all signed martingale measures with , where p≥ 1, q≥ 1 and . If there exists a with a.s., then Kp consists precisely of the random variables such that ϑ is predictable S‐integrable and for all . The duality relation corresponding to the case p=q= 2 is used to investigate the Markowitz's problem of mean–variance portfolio optimization in an incomplete market of semimartingale model via martingale/convex duality method. The duality relationship between the mean–variance efficient portfolios and the variance‐optimal signed martingale measure (VSMM) is established. It turns out that the so‐called market price of risk is just the standard deviation of the VSMM. An illustrative example of application to a geometric Lévy processes model is also given.

Suggested Citation

  • Jianming Xia & Jia‐An Yan, 2006. "Markowitz'S Portfolio Optimization In An Incomplete Market," Mathematical Finance, Wiley Blackwell, vol. 16(1), pages 203-216, January.
    • Handle: RePEc:bla:mathfi:v:16:y:2006:i:1:p:203-216
    DOI: 10.1111/j.1467-9965.2006.00268.x
    as

    Download full text from publisher

    File URL: https://doi.org/10.1111/j.1467-9965.2006.00268.x
    Download Restriction: no
    File URL: https://libkey.io/10.1111/j.1467-9965.2006.00268.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. Bernard, C. & Vanduffel, S., 2014. "Mean–variance optimal portfolios in the presence of a benchmark with applications to fraud detection," European Journal of Operational Research, Elsevier, vol. 234(2), pages 469-480.
    2. Xiangyu Cui & Duan Li & Xun Li, 2014. "Mean-Variance Policy for Discrete-time Cone Constrained Markets: The Consistency in Efficiency and Minimum-Variance Signed Supermartingale Measure," Papers 1403.0718, arXiv.org.
    3. Alev{s} v{C}ern'y & Jan Kallsen, 2007. "On the Structure of General Mean-Variance Hedging Strategies," Papers 0708.1715, arXiv.org, revised Jul 2017.
    4. Zeng, Yan & Li, Zhongfei & Lai, Yongzeng, 2013. "Time-consistent investment and reinsurance strategies for mean–variance insurers with jumps," Insurance: Mathematics and Economics, Elsevier, vol. 52(3), pages 498-507.
    5. Chen, Binbin & Huang, Shih-Feng & Pan, Guangming, 2015. "High dimensional mean–variance optimization through factor analysis," Journal of Multivariate Analysis, Elsevier, vol. 133(C), pages 140-159.
    6. Xiangyu Cui & Xun Li & Duan Li, 2013. "Unified Framework of Mean-Field Formulations for Optimal Multi-period Mean-Variance Portfolio Selection," Papers 1303.1064, arXiv.org.
    7. Yao, Haixiang & Li, Zhongfei & Chen, Shumin, 2014. "Continuous-time mean–variance portfolio selection with only risky assets," Economic Modelling, Elsevier, vol. 36(C), pages 244-251.
    8. Yuanyuan Zhang & Xiang Li & Sini Guo, 2018. "Portfolio selection problems with Markowitz’s mean–variance framework: a review of literature," Fuzzy Optimization and Decision Making, Springer, vol. 17(2), pages 125-158, June.
    9. Guo, Xianping & Ye, Liuer & Yin, George, 2012. "A mean–variance optimization problem for discounted Markov decision processes," European Journal of Operational Research, Elsevier, vol. 220(2), pages 423-429.
    10. Bai, Zhidong & Liu, Huixia & Wong, Wing-Keung, 2016. "Making Markowitz's Portfolio Optimization Theory Practically Useful," MPRA Paper 74360, University Library of Munich, Germany.
    11. Jianming Xia, 2006. "Mean-variance Hedging in the Discontinuous Case," Papers math/0607775, arXiv.org.

    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:1:p:203-216. 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.