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Portfolio selection in stochastic markets with HARA utility functions

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  • Çanakoglu, Ethem
  • Özekici, Süleyman

Abstract

In this paper, we consider the optimal portfolio selection problem where the investor maximizes the expected utility of the terminal wealth. The utility function belongs to the HARA family which includes exponential, logarithmic, and power utility functions. The main feature of the model is that returns of the risky assets and the utility function all depend on an external process that represents the stochastic market. The states of the market describe the prevailing economic, financial, social, political and other conditions that affect the deterministic and probabilistic parameters of the model. We suppose that the random changes in the market states are depicted by a Markov chain. Dynamic programming is used to obtain an explicit characterization of the optimal policy. In particular, it is shown that optimal portfolios satisfy the separation property and the composition of the risky portfolio does not depend on the wealth of the investor. We also provide an explicit construction of the optimal wealth process and use it to determine various quantities of interest. The return-risk frontiers of the terminal wealth are shown to have linear forms. Special cases are discussed together with numerical illustrations.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:ejores:v:201:y:2010:i:2:p:520-536
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. Eric Jondeau & Michael Rockinger, 2006. "Optimal Portfolio Allocation under Higher Moments," European Financial Management, European Financial Management Association, vol. 12(1), pages 29-55, January.
    4. Wolfgang Breuer & Marc Gurtler, 2006. "Performance Evaluation, Portfolio Selection, and HARA Utility," The European Journal of Finance, Taylor & Francis Journals, vol. 12(8), pages 649-669.
    5. Loistl, Otto, 1976. "The Erroneous Approximation of Expected Utility by Means of a Taylor's Series Expansion: Analytic and Computational Results," American Economic Review, American Economic Association, vol. 66(5), pages 904-910, December.
    6. Hakansson, Nils H, 1971. "On Optimal Myopic Portfolio Policies, With and Without Serial Correlation of Yields," The Journal of Business, University of Chicago Press, vol. 44(3), pages 324-334, July.
    7. Jing-Sheng Song & Paul Zipkin, 1993. "Inventory Control in a Fluctuating Demand Environment," Operations Research, INFORMS, vol. 41(2), pages 351-370, April.
    8. 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.
    9. 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.
    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. 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.
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