IDEAS home Printed from https://ideas.repec.org/p/arx/papers/1803.07720.html
   My bibliography  Save this paper

Asymptotic Optimal Portfolio in Fast Mean-reverting Stochastic Environments

Author

Listed:
  • Ruimeng Hu

Abstract

This paper studies the portfolio optimization problem when the investor's utility is general and the return and volatility of the risky asset are fast mean-reverting, which are important to capture the fast-time scale in the modeling of stock price volatility. Motivated by the heuristic derivation in [J.-P. Fouque, R. Sircar and T. Zariphopoulou, \emph{Mathematical Finance}, 2016], we propose a zeroth order strategy, and show its asymptotic optimality within a specific (smaller) family of admissible strategies under proper assumptions. This optimality result is achieved by establishing a first order approximation of the problem value associated to this proposed strategy using singular perturbation method, and estimating the risk-tolerance functions. The results are natural extensions of our previous work on portfolio optimization in a slowly varying stochastic environment [J.-P. Fouque and R. Hu, \emph{SIAM Journal on Control and Optimization}, 2017], and together they form a whole picture of analyzing portfolio optimization in both fast and slow environments.

Suggested Citation

  • Ruimeng Hu, 2018. "Asymptotic Optimal Portfolio in Fast Mean-reverting Stochastic Environments," Papers 1803.07720, arXiv.org, revised Jan 2019.
    • Handle: RePEc:arx:papers:1803.07720
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/1803.07720
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Fouque,Jean-Pierre & Papanicolaou,George & Sircar,Ronnie & Sølna,Knut, 2011. "Multiscale Stochastic Volatility for Equity, Interest Rate, and Credit Derivatives," Cambridge Books, Cambridge University Press, number 9780521843584.
    2. Thaleia Zariphopoulou, 1999. "Optimal investment and consumption models with non-linear stock dynamics," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 50(2), pages 271-296, October.
    3. George Chacko & Luis M. Viceira, 2005. "Dynamic Consumption and Portfolio Choice with Stochastic Volatility in Incomplete Markets," The Review of Financial Studies, Society for Financial Studies, vol. 18(4), pages 1369-1402.
    4. Merton, Robert C., 1971. "Optimum consumption and portfolio rules in a continuous-time model," Journal of Economic Theory, Elsevier, vol. 3(4), pages 373-413, December.
    5. Sanford J. Grossman & Zhongquan Zhou, 1993. "Optimal Investment Strategies For Controlling Drawdowns," Mathematical Finance, Wiley Blackwell, vol. 3(3), pages 241-276, July.
    6. Merton, Robert C, 1969. "Lifetime Portfolio Selection under Uncertainty: The Continuous-Time Case," The Review of Economics and Statistics, MIT Press, vol. 51(3), pages 247-257, August.
    7. Romuald Elie & Nizar Touzi, 2008. "Optimal lifetime consumption and investment under a drawdown constraint," Finance and Stochastics, Springer, vol. 12(3), pages 299-330, July.
    8. Magill, Michael J. P. & Constantinides, George M., 1976. "Portfolio selection with transactions costs," Journal of Economic Theory, Elsevier, vol. 13(2), pages 245-263, October.
    9. Markus K. Brunnermeier & Stefan Nagel, 2008. "Do Wealth Fluctuations Generate Time-Varying Risk Aversion? Micro-evidence on Individuals," American Economic Review, American Economic Association, vol. 98(3), pages 713-736, June.
    10. Cuoco, Domenico & Cvitanic, Jaksa, 1998. "Optimal consumption choices for a 'large' investor," Journal of Economic Dynamics and Control, Elsevier, vol. 22(3), pages 401-436, March.
    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. Jean-Pierre Fouque & Ruimeng Hu, 2019. "Multiscale Asymptotic Analysis for Portfolio Optimization under Stochastic Environment," Papers 1902.06883, arXiv.org, revised Sep 2019.
    2. Jean-Pierre Fouque & Ruimeng Hu, 2017. "Optimal Portfolio under Fast Mean-reverting Fractional Stochastic Environment," Papers 1706.03139, arXiv.org, revised Feb 2018.
    3. Jean-Pierre Fouque & Ruimeng Hu, 2016. "Asymptotic Optimal Strategy for Portfolio Optimization in a Slowly Varying Stochastic Environment," Papers 1603.03538, arXiv.org, revised Nov 2016.
    4. Jean-Pierre Fouque & Ruimeng Hu, 2017. "Optimal Portfolio under Fractional Stochastic Environment," Papers 1703.06969, arXiv.org, revised Dec 2017.
    5. Maxim Bichuch & Jean-Pierre Fouque, 2019. "Optimal Investment with Correlated Stochastic Volatility Factors," Papers 1908.07626, arXiv.org, revised Nov 2022.
    6. Ankush Agarwal & Ronnie Sircar, 2017. "Portfolio Benchmarking under Drawdown Constraint and Stochastic Sharpe Ratio," Working Papers hal-01388399, HAL.
    7. Ankush Agarwal & Ronnie Sircar, 2016. "Portfolio Benchmarking under Drawdown Constraint and Stochastic Sharpe Ratio," Papers 1610.08558, arXiv.org.
    8. Feyzullah Egriboyun & H. Soner, 2010. "Optimal investment strategies with a reallocation constraint," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 71(3), pages 551-585, June.
    9. Jan Kallsen & Johannes Muhle-Karbe, 2013. "The General Structure of Optimal Investment and Consumption with Small Transaction Costs," Papers 1303.3148, arXiv.org, revised May 2015.
    10. Stefan Gerhold & Paolo Guasoni & Johannes Muhle-Karbe & Walter Schachermayer, 2011. "Transaction Costs, Trading Volume, and the Liquidity Premium," Papers 1108.1167, arXiv.org, revised Jan 2013.
    11. Maxim Bichuch & Jean‐Pierre Fouque, 2023. "Optimal investment with correlated stochastic volatility factors," Mathematical Finance, Wiley Blackwell, vol. 33(2), pages 342-369, April.
    12. John Y. Campbell & Luis M. Viceira & Joshua S. White, 2003. "Foreign Currency for Long-Term Investors," Economic Journal, Royal Economic Society, vol. 113(486), pages 1-25, March.
    13. Qian Lin & Frank Riedel, 2021. "Optimal consumption and portfolio choice with ambiguous interest rates and volatility," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 71(3), pages 1189-1202, April.
    14. John Y. Campbell & Yeung Lewis Chanb & M. Viceira, 2013. "A multivariate model of strategic asset allocation," World Scientific Book Chapters, in: Leonard C MacLean & William T Ziemba (ed.), HANDBOOK OF THE FUNDAMENTALS OF FINANCIAL DECISION MAKING Part II, chapter 39, pages 809-848, World Scientific Publishing Co. Pte. Ltd..
    15. Xinfu Chen & Min Dai & Wei Jiang & Cong Qin, 2022. "Asymptotic analysis of long‐term investment with two illiquid and correlated assets," Mathematical Finance, Wiley Blackwell, vol. 32(4), pages 1133-1169, October.
    16. Jean-Pierre Fouque & Ruimeng Hu & Ronnie Sircar, 2021. "Sub- and Super-solution Approach to Accuracy Analysis of Portfolio Optimization Asymptotics in Multiscale Stochastic Factor Market," Papers 2106.11510, arXiv.org, revised Oct 2021.
    17. Guiyuan Ma & Song-Ping Zhu, 2022. "Revisiting the Merton Problem: from HARA to CARA Utility," Computational Economics, Springer;Society for Computational Economics, vol. 59(2), pages 651-686, February.
    18. Mark E. Wohar & David E. Rapach, 2005. "Return Predictability and the Implied Intertemporal Hedging Demands for Stocks and Bonds: International Evidence," Computing in Economics and Finance 2005 329, Society for Computational Economics.
    19. Baojun Bian & Xinfu Chen & Min Dai & Shuaijie Qian, 2021. "Penalty method for portfolio selection with capital gains tax," Mathematical Finance, Wiley Blackwell, vol. 31(3), pages 1013-1055, July.
    20. Michael W. Brandt & Amit Goyal & Pedro Santa-Clara & Jonathan R. Stroud, 2005. "A Simulation Approach to Dynamic Portfolio Choice with an Application to Learning About Return Predictability," The Review of Financial Studies, Society for Financial Studies, vol. 18(3), pages 831-873.

    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:1803.07720. 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.