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Optimal portfolio selection and compression in an incomplete market

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  • N. Dokuchaev
  • U. Haussmann

Abstract

We investigate an optimal investment problem with a general performance criterion which, in particular, includes discontinuous functions. Prices are modelled 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 any admissible strategy 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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  • N. Dokuchaev & U. Haussmann, 2001. "Optimal portfolio selection and compression in an incomplete market," Quantitative Finance, Taylor & Francis Journals, vol. 1(3), pages 336-345, March.
    • Handle: RePEc:taf:quantf:v:1:y:2001:i:3:p:336-345
    DOI: 10.1088/1469-7688/1/3/305
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    1. Robert C. Merton, 2005. "Theory of rational option pricing," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 8, pages 229-288, World Scientific Publishing Co. Pte. Ltd..
    2. Zhongquan Zhou, 1998. "An Equilibrium Analysis of Hedging with Liquidity Constraints, Speculation, and Government Price Subsidy in a Commodity Market," Journal of Finance, American Finance Association, vol. 53(5), pages 1705-1736, October.
    3. Jean-Paul Laurent & Huyen Pham, 1999. "Dynamic programming and mean-variance hedging," Post-Print hal-03675953, HAL.
    4. Martin Kulldorff & Ajay Khanna, 1999. "A generalization of the mutual fund theorem," Finance and Stochastics, Springer, vol. 3(2), pages 167-185.
    5. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
    6. 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.
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    Cited by:

    1. 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.
    2. Nikolai Dokuchaev, 2015. "Modelling Possibility of Short-Term Forecasting of Market Parameters for Portfolio Selection," Annals of Economics and Finance, Society for AEF, vol. 16(1), pages 143-161, May.
    3. Nikolai Dokuchaev, 2009. "Mutual Fund Theorem for continuous time markets with random coefficients," Papers 0911.3194, arXiv.org.
    4. 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.
    5. Vikranth Lokeshwar Dhandapani & Shashi Jain, 2024. "Neural Networks for Portfolio-Level Risk Management: Portfolio Compression, Static Hedging, Counterparty Credit Risk Exposures and Impact on Capital Requirement," Papers 2402.17941, arXiv.org.
    6. Nikolai Dokuchaev, 2015. "Optimal portfolio with unobservable market parameters and certainty equivalence principle," Papers 1502.02352, arXiv.org.
    7. Nikolai Dokuchaev, 2002. "Maximin setting for investment problems and fixed income management with observable but non-predictable parameters," Papers math/0207259, arXiv.org.
    8. Nikolai Dokuchaev, 2014. "Mutual Fund Theorem for continuous time markets with random coefficients," Theory and Decision, Springer, vol. 76(2), pages 179-199, February.
    9. 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.
    10. David Feldman, 2007. "Incomplete information equilibria: Separation theorems and other myths," Annals of Operations Research, Springer, vol. 151(1), pages 119-149, April.

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