IDEAS home Printed from https://ideas.repec.org/a/spr/annopr/v166y2009i1p281-29710.1007-s10479-008-0406-2.html
   My bibliography  Save this article

Portfolio selection in stochastic markets with exponential utility functions

Author

Listed:
  • Ethem Çanakoğlu
  • Süleyman Özekici

Abstract

We consider the optimal portfolio selection problem in a multiple period setting where the investor maximizes the expected utility of the terminal wealth in a stochastic market. The utility function has an exponential structure and the market states change according to a Markov chain. The states of the market describe the prevailing economic, financial, social and other conditions that affect the deterministic and probabilistic parameters of the model. This includes the distributions of the random asset returns as well as the utility function. The problem is solved using the dynamic programming approach to obtain the optimal solution and an explicit characterization of the optimal policy. We also discuss the stochastic structure of the wealth process under the optimal policy and determine various quantities of interest including its Fourier transform. The exponential return-risk frontier of the terminal wealth is shown to have a linear form. Special cases of multivariate normal and exponential returns are disussed together with a numerical illustration. Copyright Springer Science+Business Media, LLC 2009

Suggested Citation

  • Ethem Çanakoğlu & Süleyman Özekici, 2009. "Portfolio selection in stochastic markets with exponential utility functions," Annals of Operations Research, Springer, vol. 166(1), pages 281-297, February.
    • Handle: RePEc:spr:annopr:v:166:y:2009:i:1:p:281-297:10.1007/s10479-008-0406-2
    DOI: 10.1007/s10479-008-0406-2
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s10479-008-0406-2
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s10479-008-0406-2?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
    ---><---

    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. Ehrlich, Isaac & Hamlen, William Jr., 1995. "Optimal portfolio and consumption decisions in a stochastic environment with precommitment," Journal of Economic Dynamics and Control, Elsevier, vol. 19(3), pages 457-480, April.
    2. Jing-Sheng Song & Paul Zipkin, 1993. "Inventory Control in a Fluctuating Demand Environment," Operations Research, INFORMS, vol. 41(2), pages 351-370, April.
    3. Paul A. Samuelson, 2011. "Lifetime Portfolio Selection by Dynamic Stochastic Programming," World Scientific Book Chapters, in: Leonard C MacLean & Edward O Thorp & William T Ziemba (ed.), THE KELLY CAPITAL GROWTH INVESTMENT CRITERION THEORY and PRACTICE, chapter 31, pages 465-472, World Scientific Publishing Co. Pte. Ltd..
    4. Ying Hu & Peter Imkeller & Matthias Muller, 2005. "Utility maximization in incomplete markets," Papers math/0508448, arXiv.org.
    5. Ragnar Norberg, 1995. "A time‐continuous markov chain interest model with applications to insurance," Applied Stochastic Models and Data Analysis, John Wiley & Sons, vol. 11(3), pages 245-256, September.
    6. Thaleia Zariphopoulou, 2001. "A solution approach to valuation with unhedgeable risks," Finance and Stochastics, Springer, vol. 5(1), pages 61-82.
    7. Bodily, Samuel E. & White, Chelsea C., 1982. "Optimal Consumption and Portfolio Strategies in a Discrete-Time Model with Summary-Dependent Preferences," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 17(1), pages 1-14, March.
    8. Dumas, Bernard & Luciano, Elisa, 1991. "An Exact Solution to a Dynamic Portfolio Choice Problem under Transactions Costs," Journal of Finance, American Finance Association, vol. 46(2), pages 577-595, June.
    9. Tomasz Bielecki & Daniel Hernández-Hernández & Stanley R. Pliska, 1999. "Risk sensitive control of finite state Markov chains in discrete time, with applications to portfolio management," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 50(2), pages 167-188, October.
    10. 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.
    11. Gordon Pye, 1966. "A Markov Model of the Term Structure," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 80(1), pages 60-72.
    12. MOSSIN, Jan, 1968. "Optimal multiperiod portfolio policies," LIDAM Reprints CORE 19, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    13. Elton, Edwin J & Gruber, Martin J, 1974. "On the Optimality of Some Multiperiod Portfolio Selection Criteria," The Journal of Business, University of Chicago Press, vol. 47(2), pages 231-243, April.
    14. Duan Li & Wan‐Lung Ng, 2000. "Optimal Dynamic Portfolio Selection: Multiperiod Mean‐Variance Formulation," Mathematical Finance, Wiley Blackwell, vol. 10(3), pages 387-406, July.
    15. U. Çakmak & S. Özekici, 2006. "Portfolio optimization in stochastic markets," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 63(1), pages 151-168, February.
    16. Lukasz Stettner, 1999. "Risk sensitive portfolio optimization," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 50(3), pages 463-474, December.
    17. Robert J. Elliott & Rogemar S. Mamon, 2003. "A Complete Yield Curve Description Of A Markov Interest Rate Model," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 6(04), pages 317-326.
    18. Chen, Andrew H Y & Jen, Frank C & Zionts, Stanley, 1971. "The Optimal Portfolio Revision Policy," The Journal of Business, University of Chicago Press, vol. 44(1), pages 51-61, January.
    19. Tehranchi, Michael, 2004. "Explicit solutions of some utility maximization problems in incomplete markets," Stochastic Processes and their Applications, Elsevier, vol. 114(1), pages 109-125, November.
    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. Bodnar, Taras & Parolya, Nestor & Schmid, Wolfgang, 2015. "On the exact solution of the multi-period portfolio choice problem for an exponential utility under return predictability," European Journal of Operational Research, Elsevier, vol. 246(2), pages 528-542.
    2. Reza Keykhaei, 2020. "Portfolio selection in a regime switching market with a bankruptcy state and an uncertain exit-time: multi-period mean–variance formulation," Operational Research, Springer, vol. 20(3), pages 1231-1254, September.
    3. Pelin Canbolat, 2014. "Optimal halting policies in Markov population decision chains with constant risk posture," Annals of Operations Research, Springer, vol. 222(1), pages 227-237, November.

    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. U. Çakmak & S. Özekici, 2006. "Portfolio optimization in stochastic markets," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 63(1), pages 151-168, February.
    2. Çanakoglu, Ethem & Özekici, Süleyman, 2010. "Portfolio selection in stochastic markets with HARA utility functions," European Journal of Operational Research, Elsevier, vol. 201(2), pages 520-536, March.
    3. Celikyurt, U. & Ozekici, S., 2007. "Multiperiod portfolio optimization models in stochastic markets using the mean-variance approach," European Journal of Operational Research, Elsevier, vol. 179(1), pages 186-202, May.
    4. Zhang, Xili & Zhang, Weiguo & Xiao, Weilin, 2013. "Multi-period portfolio optimization under possibility measures," Economic Modelling, Elsevier, vol. 35(C), pages 401-408.
    5. Bauder, David & Bodnar, Taras & Parolya, Nestor & Schmid, Wolfgang, 2020. "Bayesian inference of the multi-period optimal portfolio for an exponential utility," Journal of Multivariate Analysis, Elsevier, vol. 175(C).
    6. Bodnar, Taras & Parolya, Nestor & Schmid, Wolfgang, 2015. "On the exact solution of the multi-period portfolio choice problem for an exponential utility under return predictability," European Journal of Operational Research, Elsevier, vol. 246(2), pages 528-542.
    7. Dokuchaev, Nikolai, 2007. "Discrete time market with serial correlations and optimal myopic strategies," European Journal of Operational Research, Elsevier, vol. 177(2), pages 1090-1104, March.
    8. Leippold, Markus & Trojani, Fabio & Vanini, Paolo, 2004. "A geometric approach to multiperiod mean variance optimization of assets and liabilities," Journal of Economic Dynamics and Control, Elsevier, vol. 28(6), pages 1079-1113, March.
    9. Dokuchaev, Nikolai, 2010. "Optimality of myopic strategies for multi-stock discrete time market with management costs," European Journal of Operational Research, Elsevier, vol. 200(2), pages 551-556, January.
    10. Yu, Mei & Takahashi, Satoru & Inoue, Hiroshi & Wang, Shouyang, 2010. "Dynamic portfolio optimization with risk control for absolute deviation model," European Journal of Operational Research, Elsevier, vol. 201(2), pages 349-364, March.
    11. Buckley, Winston S. & Brown, Garfield O. & Marshall, Mario, 2012. "A mispricing model of stocks under asymmetric information," European Journal of Operational Research, Elsevier, vol. 221(3), pages 584-592.
    12. Ruili Sun & Tiefeng Ma & Shuangzhe Liu & Milind Sathye, 2019. "Improved Covariance Matrix Estimation for Portfolio Risk Measurement: A Review," JRFM, MDPI, vol. 12(1), pages 1-34, March.
    13. Briec, Walter & Kerstens, Kristiaan, 2009. "Multi-horizon Markowitz portfolio performance appraisals: A general approach," Omega, Elsevier, vol. 37(1), pages 50-62, February.
    14. Shi, Yun, 2020. "Timing Idiosyncratic Volatility and Dynamic Asset Allocation," SocArXiv 9kber, Center for Open Science.
    15. 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.
    16. Alexandra Rodkina & Nikolai Dokuchaev, 2014. "On asymptotic optimality of Merton's myopic portfolio strategies for discrete time market," Papers 1403.4329, arXiv.org, revised Nov 2014.
    17. Ying Fu & Kien Ng & Boray Huang & Huei Huang, 2015. "Portfolio optimization with transaction costs: a two-period mean-variance model," Annals of Operations Research, Springer, vol. 233(1), pages 135-156, October.
    18. Castellano, Rosella & Cerqueti, Roy, 2014. "Mean–Variance portfolio selection in presence of infrequently traded stocks," European Journal of Operational Research, Elsevier, vol. 234(2), pages 442-449.
    19. Penikas, Henry, 2010. "Copula-Models in Foreign Exchange Risk-Management of a Bank," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 17(1), pages 62-87.
    20. Fu, Chenpeng & Lari-Lavassani, Ali & Li, Xun, 2010. "Dynamic mean-variance portfolio selection with borrowing constraint," European Journal of Operational Research, Elsevier, vol. 200(1), pages 312-319, January.

    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:spr:annopr:v:166:y:2009:i:1:p:281-297:10.1007/s10479-008-0406-2. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.