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Use of stochastic and mathematical programming in portfolio theory and practice

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  • William Ziemba

Abstract

Standard finance portfolio theory draws graphs and writes equations usually with no constraints and frequently in the univariate case. However, in reality, there are multivariate random variables and multivariate asset weights to determine with constraints. Also there are the effects of transaction costs on asset prices in the theory and calculation of optimal portfolios in the static and dynamic cases. There we use various stochastic programming, linear complementary, quadratic programming and nonlinear programming problems. This paper begins with the simplest problems and builds the theory to the more complex cases and then applies it to real financial asset allocation problems, hedge funds and professional racetrack betting. Copyright Springer Science+Business Media, LLC 2009

Suggested Citation

  • William Ziemba, 2009. "Use of stochastic and mathematical programming in portfolio theory and practice," Annals of Operations Research, Springer, vol. 166(1), pages 5-22, February.
    • Handle: RePEc:spr:annopr:v:166:y:2009:i:1:p:5-22:10.1007/s10479-008-0441-z
    DOI: 10.1007/s10479-008-0441-z
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    References listed on IDEAS

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    1. J. G. Kallberg & W. T. Ziemba, 1983. "Comparison of Alternative Utility Functions in Portfolio Selection Problems," Management Science, INFORMS, vol. 29(11), pages 1257-1276, November.
    2. Donald B. Hausch & Victor S. Y. Lo & William T. Ziemba, 2008. "Introduction to the Efficiency of Racetrack Betting Markets in England," World Scientific Book Chapters, in: Donald B Hausch & Victor SY Lo & William T Ziemba (ed.), Efficiency Of Racetrack Betting Markets, chapter 51, pages 529-531, World Scientific Publishing Co. Pte. Ltd..
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    6. William F. Sharpe, 1964. "Capital Asset Prices: A Theory Of Market Equilibrium Under Conditions Of Risk," Journal of Finance, American Finance Association, vol. 19(3), pages 425-442, September.
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    Cited by:

    1. I-Chen Lu & Kai-Hong Tee & Baibing Li, 2019. "Asset allocation with multiple analysts’ views: a robust approach," Journal of Asset Management, Palgrave Macmillan, vol. 20(3), pages 215-228, May.
    2. Bae, Geum Il & Kim, Woo Chang & Mulvey, John M., 2014. "Dynamic asset allocation for varied financial markets under regime switching framework," European Journal of Operational Research, Elsevier, vol. 234(2), pages 450-458.

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