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Nonparametric Kernel‐Based Sequential Investment Strategies

Author

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  • László Györfi
  • Gábor Lugosi
  • Frederic Udina

Abstract

The purpose of this paper is to introduce sequential investment strategies that guarantee an optimal rate of growth of the capital, under minimal assumptions on the behavior of the market. The new strategies are analyzed both theoretically and empirically. The theoretical results show that the asymptotic rate of growth matches the optimal one that one could achieve with a full knowledge of the statistical properties of the underlying process generating the market, under the only assumption that the market is stationary and ergodic. The empirical results show that the performance of the proposed investment strategies measured on past nyse and currency exchange data is solid, and sometimes even spectacular.

Suggested Citation

  • László Györfi & Gábor Lugosi & Frederic Udina, 2006. "Nonparametric Kernel‐Based Sequential Investment Strategies," Mathematical Finance, Wiley Blackwell, vol. 16(2), pages 337-357, April.
    • Handle: RePEc:bla:mathfi:v:16:y:2006:i:2:p:337-357
    DOI: 10.1111/j.1467-9965.2006.00274.x
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    Cited by:

    1. Guy Uziel & Ran El-Yaniv, 2017. "Growth-Optimal Portfolio Selection under CVaR Constraints," Papers 1705.09800, arXiv.org.
    2. Ormos, Mihály & Urbán, András & Zoltán, Tamás, 2009. "Logoptimális portfóliók empirikus vizsgálata [Empirical analysis of log-optimal portfolios]," Közgazdasági Szemle (Economic Review - monthly of the Hungarian Academy of Sciences), Közgazdasági Szemle Alapítvány (Economic Review Foundation), vol. 0(1), pages 1-18.
    3. Seung-Hyun Moon & Yourim Yoon, 2022. "Genetic Mean Reversion Strategy for Online Portfolio Selection with Transaction Costs," Mathematics, MDPI, vol. 10(7), pages 1-20, March.
    4. 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.
    5. Bin Li & Dingjiang Huang & Steven C. H. Hoi, 2013. "CORN: Correlation-Driven Nonparametric Learning Approach for Portfolio Selection -- an Online Appendix," Papers 1306.1378, arXiv.org.
    6. Ansgar Steland, 2018. "Shrinkage for covariance estimation: asymptotics, confidence intervals, bounds and applications in sensor monitoring and finance," Statistical Papers, Springer, vol. 59(4), pages 1441-1462, December.
    7. Sancetta, A., 2007. "Online Forecast Combination for Dependent Heterogeneous Data," Cambridge Working Papers in Economics 0718, Faculty of Economics, University of Cambridge.
    8. Bin Li & Steven C. H. Hoi, 2012. "Online Portfolio Selection: A Survey," Papers 1212.2129, arXiv.org, revised May 2013.
    9. 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.
    10. Vladimir V'yugin, 2014. "Log-Optimal Portfolio Selection Using the Blackwell Approachability Theorem," Papers 1410.5996, arXiv.org, revised Jun 2015.
    11. Roch, Oriol, 2013. "Histogram-based prediction of directional price relatives," Finance Research Letters, Elsevier, vol. 10(3), pages 110-115.
    12. Guo, Sini & Gu, Jia-Wen & Fok, Christopher H. & Ching, Wai-Ki, 2023. "Online portfolio selection with state-dependent price estimators and transaction costs," European Journal of Operational Research, Elsevier, vol. 311(1), pages 333-353.
    13. Zhengyao Jiang & Dixing Xu & Jinjun Liang, 2017. "A Deep Reinforcement Learning Framework for the Financial Portfolio Management Problem," Papers 1706.10059, arXiv.org, revised Jul 2017.
    14. Ting-Kam Leonard Wong, 2015. "Universal portfolios in stochastic portfolio theory," Papers 1510.02808, arXiv.org, revised Dec 2016.
    15. Seung-Hyun Moon & Yong-Hyuk Kim & Byung-Ro Moon, 2019. "Empirical investigation of state-of-the-art mean reversion strategies for equity markets," Papers 1909.04327, arXiv.org.
    16. Yang Wang & Dong Wang & Yaodong Wang & You Zhang, 2018. "RACORN-K: Risk-Aversion Pattern Matching-based Portfolio Selection," Papers 1802.10244, arXiv.org.
    17. Vajda, István & Ottucsák, György, 2006. "Empirikus portfólióstratégiák [Empirical portfolio strategies]," Közgazdasági Szemle (Economic Review - monthly of the Hungarian Academy of Sciences), Közgazdasági Szemle Alapítvány (Economic Review Foundation), vol. 0(7), pages 624-640.
    18. Ottucsák György & Vajda István, 2007. "An asymptotic analysis of the mean-variance portfolio selection," Statistics & Risk Modeling, De Gruyter, vol. 25(1/2007), pages 1-24, January.
    19. Shuo Sun & Rundong Wang & Bo An, 2021. "Reinforcement Learning for Quantitative Trading," Papers 2109.13851, arXiv.org.
    20. Bin Li & Steven C. H. Hoi, 2012. "On-Line Portfolio Selection with Moving Average Reversion," Papers 1206.4626, arXiv.org.
    21. Man Yiu Tsang & Tony Sit & Hoi Ying Wong, 2022. "Adaptive Robust Online Portfolio Selection," Papers 2206.01064, arXiv.org.
    22. Ha, Youngmin & Zhang, Hai, 2020. "Algorithmic trading for online portfolio selection under limited market liquidity," European Journal of Operational Research, Elsevier, vol. 286(3), pages 1033-1051.
    23. Györfi László & Udina Frederic & Walk Harro, 2008. "Nonparametric nearest neighbor based empirical portfolio selection strategies," Statistics & Risk Modeling, De Gruyter, vol. 26(2), pages 145-157, March.

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