IDEAS home Printed from https://ideas.repec.org/a/eee/ecmode/v27y2010i3p678-686.html
   My bibliography  Save this article

On mean-variance portfolio selection under a hidden Markovian regime-switching model

Author

Listed:
  • Elliott, Robert J.
  • Siu, Tak Kuen
  • Badescu, Alex

Abstract

We study a mean-variance portfolio selection problem under a hidden Markovian regime-switching Black-Scholes-Merton economy. Under this model, the appreciation rate of a risky share is modulated by a continuous-time, finite-state hidden Markov chain whose states represent different states of an economy. We consider the general situation where an economic agent cannot observe the "true" state of the underlying economy and wishes to minimize the variance of the terminal wealth for a fixed level of expected terminal wealth with access only to information about the price processes. By exploiting the separation principle, we discuss the mean-variance portfolio selection problem and the filtering-estimation problem separately. We determine an explicit solution to the mean-variance problem using the stochastic maximum principle so that we do not need the assumption of Markovian controls. We also provide robust estimates of the hidden state of the chain and develop a robust filter-based EM algorithm for online recursive estimates of the unknown parameters in the model. This simplifies the filtering-estimation problem.

Suggested Citation

  • Elliott, Robert J. & Siu, Tak Kuen & Badescu, Alex, 2010. "On mean-variance portfolio selection under a hidden Markovian regime-switching model," Economic Modelling, Elsevier, vol. 27(3), pages 678-686, May.
  • Handle: RePEc:eee:ecmode:v:27:y:2010:i:3:p:678-686
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0264-9993(10)00008-8
    Download Restriction: Full text for ScienceDirect subscribers only

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Robert J. Elliott & Leunglung Chan & Tak Kuen Siu, 2005. "Option pricing and Esscher transform under regime switching," Annals of Finance, Springer, vol. 1(4), pages 423-432, October.
    2. Robert J. Elliott & John van der Hoek, 1997. "An application of hidden Markov models to asset allocation problems (*)," Finance and Stochastics, Springer, vol. 1(3), pages 229-238.
    3. Harry Markowitz, 1952. "Portfolio Selection," Journal of Finance, American Finance Association, vol. 7(1), pages 77-91, March.
    4. Dembo, A. & Zeitouni, O., 1986. "Parameter estimation of partially observed continuous time stochastic processes via the EM algorithm," Stochastic Processes and their Applications, Elsevier, vol. 23(1), pages 91-113, October.
    5. William F. Sharpe, 1964. "Capital Asset Prices: A Theory Of Market Equilibrium Under Conditions Of Risk," Journal of Finance, American Finance Association, vol. 19(3), pages 425-442, September.
    6. N. El Karoui & S. Peng & M. C. Quenez, 1997. "Backward Stochastic Differential Equations in Finance," Mathematical Finance, Wiley Blackwell, vol. 7(1), pages 1-71.
    7. X. Guo, 2001. "Information and option pricings," Quantitative Finance, Taylor & Francis Journals, vol. 1(1), pages 38-44.
    8. Bong-Gyu Jang & Hyeng Keun Koo & Hong Liu & Mark Loewenstein, 2007. "Liquidity Premia and Transaction Costs," Journal of Finance, American Finance Association, vol. 62(5), pages 2329-2366, October.
    9. Naik, Vasanttilak, 1993. " Option Valuation and Hedging Strategies with Jumps in the Volatility of Asset Returns," Journal of Finance, American Finance Association, vol. 48(5), pages 1969-1984, December.
    10. Christina Erlwein & Rogemar Mamon, 2009. "An online estimation scheme for a Hull–White model with HMM-driven parameters," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 18(1), pages 87-107, March.
    11. Elliott, R. J. & Malcolm, W. P. & Tsoi, Allanus H., 2003. "Robust parameter estimation for asset price models with Markov modulated volatilities," Journal of Economic Dynamics and Control, Elsevier, vol. 27(8), pages 1391-1409, June.
    12. Michael J. Brennan & Yihong Xia, 2002. "Dynamic Asset Allocation under Inflation," Journal of Finance, American Finance Association, vol. 57(3), pages 1201-1238, June.
    13. Jörn Sass & Ulrich Haussmann, 2004. "Optimizing the terminal wealth under partial information: The drift process as a continuous time Markov chain," Finance and Stochastics, Springer, vol. 8(4), pages 553-577, November.
    14. Merton, Robert C., 1980. "On estimating the expected return on the market : An exploratory investigation," Journal of Financial Economics, Elsevier, vol. 8(4), pages 323-361, December.
    15. Hamilton, James D, 1989. "A New Approach to the Economic Analysis of Nonstationary Time Series and the Business Cycle," Econometrica, Econometric Society, vol. 57(2), pages 357-384, March.
    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. Hsu, Yuan-Lin & Lin, Shih-Kuei & Hung, Ming-Chin & Huang, Tzu-Hui, 2016. "Empirical analysis of stock indices under a regime-switching model with dependent jump size risks," Economic Modelling, Elsevier, vol. 54(C), pages 260-275.
    2. Li, Ting & Zhang, Weiguo & Xu, Weijun, 2013. "Fuzzy possibilistic portfolio selection model with VaR constraint and risk-free investment," Economic Modelling, Elsevier, vol. 31(C), pages 12-17.
    3. Daniela Neykova & Marcos Escobar & Rudi Zagst, 2015. "Optimal investment in multidimensional Markov-modulated affine models," Annals of Finance, Springer, vol. 11(3), pages 503-530, November.
    4. Liang, Zongxia & Song, Min, 2015. "Time-consistent reinsurance and investment strategies for mean–variance insurer under partial information," Insurance: Mathematics and Economics, Elsevier, vol. 65(C), pages 66-76.
    5. Levy, Moshe & Kaplanski, Guy, 2015. "Portfolio selection in a two-regime world," European Journal of Operational Research, Elsevier, vol. 242(2), pages 514-524.
    6. 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.
    7. repec:spr:opsear:v:54:y:2017:i:3:d:10.1007_s12597-016-0289-y is not listed on IDEAS
    8. Yao, Haixiang & Zeng, Yan & Chen, Shumin, 2013. "Multi-period mean–variance asset–liability management with uncontrolled cash flow and uncertain time-horizon," Economic Modelling, Elsevier, vol. 30(C), pages 492-500.

    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:eee:ecmode:v:27:y:2010:i:3:p:678-686. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Dana Niculescu). General contact details of provider: http://www.elsevier.com/locate/inca/30411 .

    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 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.

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

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.