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Optimal portfolio selection and compression in an incomplete market


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  • Nikolai Dokuchaev
  • Ulrich Haussmann


We investigate an optimal investment problem with a general performance criterion which, in particular, includes discontinuous functions. Prices are modeled as diffusions and the market is incomplete. We find an explicit solution for the case of limited diversification of the portfolio, i.e. for the portfolio compression problem. By this we mean that an admissible strategies may include no more than m different stocks concurrently, where m may be less than the total number n of available stocks.

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Paper provided by in its series Papers with number math/0207260.

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Date of creation: Jul 2002
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Publication status: Published in Quantitative Finance 1(2001), iss. 3, 336-345
Handle: RePEc:arx:papers:math/0207260

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  1. Martin Kulldorff & Ajay Khanna, 1999. "A generalization of the mutual fund theorem," Finance and Stochastics, Springer, Springer, vol. 3(2), pages 167-185.
  2. Robert C. Merton, 1973. "Theory of Rational Option Pricing," Bell Journal of Economics, The RAND Corporation, The RAND Corporation, vol. 4(1), pages 141-183, Spring.
  3. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, University of Chicago Press, vol. 81(3), pages 637-54, May-June.
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Cited by:
  1. Nikolai Dokuchaev, 2014. "Mutual Fund Theorem for continuous time markets with random coefficients," Theory and Decision, Springer, Springer, vol. 76(2), pages 179-199, February.
  2. Alexandra Rodkina & Nikolai Dokuchaev, 2014. "On asymptotic optimality of Merton's myopic portfolio strategies for discrete time market," Papers 1403.4329,
  3. Nikolai Dokuchaev, 2002. "Maximin setting for investment problems and fixed income management with observable but non-predictable parameters," Papers math/0207259,
  4. Dokuchaev, Nikolai, 2007. "Discrete time market with serial correlations and optimal myopic strategies," European Journal of Operational Research, Elsevier, Elsevier, vol. 177(2), pages 1090-1104, March.
  5. Nikolai Dokuchaev, 2009. "Mutual Fund Theorem for continuous time markets with random coefficients," Papers 0911.3194,


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