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Stochastic Nonstationary Optimization for Finding Universal Portfolios

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  • Alexei Gaivoronski
  • Fabio Stella

Abstract

We apply ideas from stochastic optimization for defining universal portfolios. Universal portfolios are that class of portfolios which are constructed directly from the available observations of the stocks behavior without any assumptions about their statistical properties. Cover [7] has shown that one can construct such portfolio using only observations of the past stock prices which generates the same asymptotic wealth growth as the best constant rebalanced portfolio which is constructed with the full knowledge of the future stock market behavior. In this paper we construct universal portfolios using a different set of ideas drawn from nonstationary stochastic optimization. Our portfolios yield the same asymptotic growth of wealth as the best constant rebalanced portfolio constructed with the perfect knowledge of the future and they are less demanding computationally compared to previously known universal portfolios. We also present computational evidence using New York Stock Exchange data which shows, among other things, superior performance of portfolios which explicitly take into account possible nonstationary market behavior. Copyright Kluwer Academic Publishers 2000

Suggested Citation

  • Alexei Gaivoronski & Fabio Stella, 2000. "Stochastic Nonstationary Optimization for Finding Universal Portfolios," Annals of Operations Research, Springer, vol. 100(1), pages 165-188, December.
    • Handle: RePEc:spr:annopr:v:100:y:2000:i:1:p:165-188:10.1023/a:1019271201970
    DOI: 10.1023/A:1019271201970
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    Citations

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    Cited by:

    1. James Chok & Geoffrey M. Vasil, 2023. "Convex optimization over a probability simplex," Papers 2305.09046, arXiv.org.
    2. Jin’an He & Shicheng Yin & Fangping Peng, 2024. "Weak aggregating specialist algorithm for online portfolio selection," Computational Economics, Springer;Society for Computational Economics, vol. 63(6), pages 2405-2434, June.
    3. Guo, Sini & Gu, Jia-Wen & Ching, Wai-Ki, 2021. "Adaptive online portfolio selection with transaction costs," European Journal of Operational Research, Elsevier, vol. 295(3), pages 1074-1086.
    4. James DiLellio, 2015. "A Kalman filter control technique in mean-variance portfolio management," Journal of Economics and Finance, Springer;Academy of Economics and Finance, vol. 39(2), pages 235-261, April.
    5. Xingyu Yang & Jin’an He & Hong Lin & Yong Zhang, 2020. "Boosting Exponential Gradient Strategy for Online Portfolio Selection: An Aggregating Experts’ Advice Method," Computational Economics, Springer;Society for Computational Economics, vol. 55(1), pages 231-251, January.
    6. Shuo Sun & Rundong Wang & Bo An, 2021. "Reinforcement Learning for Quantitative Trading," Papers 2109.13851, arXiv.org.
    7. Esther Mohr & Robert Dochow, 2017. "Risk management strategies for finding universal portfolios," Annals of Operations Research, Springer, vol. 256(1), pages 129-147, September.
    8. J. D. M. Yamim & C. C. H. Borges & R. F. Neto, 2023. "Portfolio Optimization Via Online Gradient Descent and Risk Control," Computational Economics, Springer;Society for Computational Economics, vol. 62(1), pages 361-381, June.
    9. Jin’an He & Fangping Peng & Xiuying Xie, 2024. "Risk-adjusted exponential gradient strategies for online portfolio selection," Journal of Combinatorial Optimization, Springer, vol. 48(1), pages 1-25, August.
    10. Gaivoronski, Alexei A. & Krylov, Sergiy & van der Wijst, Nico, 2005. "Optimal portfolio selection and dynamic benchmark tracking," European Journal of Operational Research, Elsevier, vol. 163(1), pages 115-131, May.
    11. Sjur Flåm, 2010. "Portfolio management without probabilities or statistics," Annals of Finance, Springer, vol. 6(3), pages 357-368, July.
    12. Roujia Li & Jia Liu, 2022. "Online Portfolio Selection with Long-Short Term Forecasting," SN Operations Research Forum, Springer, vol. 3(4), pages 1-15, December.
    13. Yong Zhang & Jiahao Li & Xingyu Yang & Jianliang Zhang, 2024. "Competitive Online Strategy Based on Improved Exponential Gradient Expert and Aggregating Method," Computational Economics, Springer;Society for Computational Economics, vol. 64(2), pages 789-814, August.
    14. Yong Zhang & Xingyu Yang, 2017. "Online Portfolio Selection Strategy Based on Combining Experts’ Advice," Computational Economics, Springer;Society for Computational Economics, vol. 50(1), pages 141-159, June.
    15. Gaivoronski, Alexei A. & Stella, Fabio, 2003. "On-line portfolio selection using stochastic programming," Journal of Economic Dynamics and Control, Elsevier, vol. 27(6), pages 1013-1043, April.
    16. Yong Zhang & Hong Lin & Lina Zheng & Xingyu Yang, 2022. "Adaptive online portfolio strategy based on exponential gradient updates," Journal of Combinatorial Optimization, Springer, vol. 43(3), pages 672-696, April.

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