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Along but beyond mean-variance: Utility maximization in a semimartingale model

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  • Huhtala, Heli

    ()
    (Bank of Finland Research)

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    Abstract

    It is well known that under certain assumptions the strategy of an investor maximizing his expected utility coincides with the mean-variance optimal strategy. In this paper we show that the two strategies are not equal in general and find the connection between a utility maximizing and a mean-variance optimal strategy in a continuous semimartingale model. That is done by showing that the utility maximizing strategy of a CARA investor can be expressed in terms of expectation and the expected quadratic variation of the underlying price process. It coincides with the mean-variance optimal strategy if the underlying price process is a local martingale.

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    File URL: http://www.suomenpankki.fi/en/julkaisut/tutkimukset/keskustelualoitteet/Documents/0805netti.pdf
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    Bibliographic Info

    Paper provided by Bank of Finland in its series Research Discussion Papers with number 5/2008.

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    Length: 29 pages
    Date of creation: 11 Mar 2008
    Date of revision:
    Handle: RePEc:hhs:bofrdp:2008_005

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    Postal: Bank of Finland, P.O. Box 160, FI-00101 Helsinki, Finland
    Web page: http://www.suomenpankki.fi/en/
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    Related research

    Keywords: mean-variance portfolios; utility maximization; dynamic portfolio selection; quadratic variation;

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    1. Philippe Artzner & Freddy Delbaen & Jean-Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, Wiley Blackwell, vol. 9(3), pages 203-228.
    2. Torben G. Andersen & Tim Bollerslev & Francis X. Diebold & Paul Labys, 1999. "Exchange Rate Returns Standardized by Realized Volatility are (Nearly) Gaussian," New York University, Leonard N. Stern School Finance Department Working Paper Seires, New York University, Leonard N. Stern School of Business- 99-060, New York University, Leonard N. Stern School of Business-.
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    11. Harrison, J. Michael & Pliska, Stanley R., 1981. "Martingales and stochastic integrals in the theory of continuous trading," Stochastic Processes and their Applications, Elsevier, vol. 11(3), pages 215-260, August.
    12. Cox, John C. & Huang, Chi-fu, 1989. "Optimal consumption and portfolio policies when asset prices follow a diffusion process," Journal of Economic Theory, Elsevier, vol. 49(1), pages 33-83, October.
    13. Martin Schweizer & HuyËn Pham & (*), Thorsten RheinlÄnder, 1998. "Mean-variance hedging for continuous processes: New proofs and examples," Finance and Stochastics, Springer, vol. 2(2), pages 173-198.
    14. S. D. Jacka, 1992. "A Martingale Representation Result and an Application to Incomplete Financial Markets," Mathematical Finance, Wiley Blackwell, Wiley Blackwell, vol. 2(4), pages 239-250.
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