IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2103.10925.html
   My bibliography  Save this paper

Functional portfolio optimization in stochastic portfolio theory

Author

Listed:
  • Steven Campbell
  • Ting-Kam Leonard Wong

Abstract

In this paper we develop a concrete and fully implementable approach to the optimization of functionally generated portfolios in stochastic portfolio theory. The main idea is to optimize over a family of rank-based portfolios parameterized by an exponentially concave function on the unit interval. This choice can be motivated by the long term stability of the capital distribution observed in large equity markets, and allows us to circumvent the curse of dimensionality. The resulting optimization problem, which is convex, allows for various regularizations and constraints to be imposed on the generating function. We prove an existence and uniqueness result for our optimization problem and provide a stability estimate in terms of a Wasserstein metric of the input measure. Then, we formulate a discretization which can be implemented numerically using available software packages and analyze its approximation error. Finally, we present empirical examples using CRSP data from the US stock market, including the performance of the portfolios allowing for dividends, defaults, and transaction costs.

Suggested Citation

  • Steven Campbell & Ting-Kam Leonard Wong, 2021. "Functional portfolio optimization in stochastic portfolio theory," Papers 2103.10925, arXiv.org, revised Oct 2021.
    • Handle: RePEc:arx:papers:2103.10925
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2103.10925
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Daniel Fernholz & Ioannis Karatzas, 2010. "On optimal arbitrage," Papers 1010.4987, arXiv.org.
    2. Ali Al-Aradi & Sebastian Jaimungal, 2018. "Outperformance and Tracking: Dynamic Asset Allocation for Active and Passive Portfolio Management," Applied Mathematical Finance, Taylor & Francis Journals, vol. 25(3), pages 268-294, May.
    3. Robert Fernholz, 2001. "Equity portfolios generated by functions of ranked market weights," Finance and Stochastics, Springer, vol. 5(4), pages 469-486.
    4. Ali Al-Aradi & Sebastian Jaimungal, 2018. "Outperformance and Tracking: Dynamic Asset Allocation for Active and Passive Portfolio Management," Papers 1803.05819, arXiv.org, revised Jul 2018.
    5. Erhan Bayraktar & Yu-Jui Huang & Qingshuo Song, 2010. "Outperforming the market portfolio with a given probability," Papers 1006.3224, arXiv.org, revised Aug 2012.
    6. Robert Fernholz, 1999. "Portfolio Generating Functions," World Scientific Book Chapters, in: Marco Avellaneda (ed.), Quantitative Analysis In Financial Markets Collected Papers of the New York University Mathematical Finance Seminar, chapter 15, pages 344-367, World Scientific Publishing Co. Pte. Ltd..
    7. Thomas M. Cover, 1991. "Universal Portfolios," Mathematical Finance, Wiley Blackwell, vol. 1(1), pages 1-29, January.
    Full references (including those not matched with items on IDEAS)

    Citations

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


    Cited by:

    1. David Itkin & Martin Larsson, 2021. "Open Markets and Hybrid Jacobi Processes," Papers 2110.14046, arXiv.org, revised Mar 2024.
    2. David Itkin & Benedikt Koch & Martin Larsson & Josef Teichmann, 2022. "Ergodic robust maximization of asymptotic growth under stochastic volatility," Papers 2211.15628, arXiv.org.
    3. Andrew L. Allan & Christa Cuchiero & Chong Liu & David J. Promel, 2021. "Model-free Portfolio Theory: A Rough Path Approach," Papers 2109.01843, arXiv.org, revised Oct 2022.
    4. Erhan Bayraktar & Donghan Kim & Abhishek Tilva, 2022. "Arbitrage theory in a market of stochastic dimension," Papers 2212.04623, arXiv.org, revised Jun 2023.
    5. Christa Cuchiero & Janka Moller, 2023. "Signature Methods in Stochastic Portfolio Theory," Papers 2310.02322, arXiv.org, revised Mar 2024.

    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. Alexander Vervuurt, 2015. "Topics in Stochastic Portfolio Theory," Papers 1504.02988, arXiv.org.
    2. Alexander Vervuurt & Ioannis Karatzas, 2015. "Diversity-weighted portfolios with negative parameter," Annals of Finance, Springer, vol. 11(3), pages 411-432, November.
    3. Alexander Vervuurt & Ioannis Karatzas, 2015. "Diversity-Weighted Portfolios with Negative Parameter," Papers 1504.01026, arXiv.org, revised Jul 2015.
    4. Andrew L. Allan & Christa Cuchiero & Chong Liu & David J. Prömel, 2023. "Model‐free portfolio theory: A rough path approach," Mathematical Finance, Wiley Blackwell, vol. 33(3), pages 709-765, July.
    5. Ioannis Karatzas & Johannes Ruf, 2017. "Trading strategies generated by Lyapunov functions," Finance and Stochastics, Springer, vol. 21(3), pages 753-787, July.
    6. Johannes Ruf & Kangjianan Xie, 2018. "Generalised Lyapunov Functions and Functionally Generated Trading Strategies," Papers 1801.07817, arXiv.org.
    7. Sebastian Jaimungal, 2022. "Reinforcement learning and stochastic optimisation," Finance and Stochastics, Springer, vol. 26(1), pages 103-129, January.
    8. Erhan Bayraktar & Donghan Kim & Abhishek Tilva, 2023. "Quantifying dimensional change in stochastic portfolio theory," Papers 2303.00858, arXiv.org, revised Apr 2023.
    9. Kangjianan Xie, 2019. "Leakage of rank-dependent functionally generated trading strategies," Papers 1912.04221, arXiv.org.
    10. Kardaras, Constantinos & Robertson, Scott, 2012. "Robust maximization of asymptotic growth," LSE Research Online Documents on Economics 44994, London School of Economics and Political Science, LSE Library.
    11. Karatzas, Ioannis & Ruf, Johannes, 2017. "Trading strategies generated by Lyapunov functions," LSE Research Online Documents on Economics 69177, London School of Economics and Political Science, LSE Library.
    12. Ali Al-Aradi & Sebastian Jaimungal, 2019. "Active and Passive Portfolio Management with Latent Factors," Papers 1903.06928, arXiv.org.
    13. Christa Cuchiero & Walter Schachermayer & Ting-Kam Leonard Wong, 2016. "Cover's universal portfolio, stochastic portfolio theory and the numeraire portfolio," Papers 1611.09631, arXiv.org.
    14. Zihao Zhang & Stefan Zohren & Stephen Roberts, 2020. "Deep Learning for Portfolio Optimization," Papers 2005.13665, arXiv.org, revised Jan 2021.
    15. Donghan Kim, 2019. "Open Markets," Papers 1912.13110, arXiv.org.
    16. Ali Al-Aradi & Sebastian Jaimungal, 2020. "A Variational Analysis Approach to Solving the Merton Problem," Papers 2003.08450, arXiv.org.
    17. Constantinos Kardaras & Scott Robertson, 2018. "Ergodic robust maximization of asymptotic growth," Papers 1801.06425, arXiv.org.
    18. Soumik Pal & Ting-Kam Leonard Wong, 2016. "Exponentially concave functions and a new information geometry," Papers 1605.05819, arXiv.org, revised May 2017.
    19. Ioannis Karatzas & Johannes Ruf, 2016. "Trading Strategies Generated by Lyapunov Functions," Papers 1603.08245, arXiv.org.
    20. Michael Heinrich Baumann, 2022. "Beating the market? A mathematical puzzle for market efficiency," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 45(1), pages 279-325, June.

    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:arx:papers:2103.10925. 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.