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Learning Threshold-Type Investment Strategies with Stochastic Gradient Method

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  • Zsolt Nika
  • Mikl'os R'asonyi

Abstract

In online portfolio optimization the investor makes decisions based on new, continuously incoming information on financial assets (typically their prices). In our study we consider a learning algorithm, namely the Kiefer--Wolfowitz version of the Stochastic Gradient method, that converges to the log-optimal solution in the threshold-type, buy-and-sell strategy class. The systematic study of this method is novel in the field of portfolio optimization; we aim to establish the theory and practice of Stochastic Gradient algorithm used on parametrized trading strategies. We demonstrate on a wide variety of stock price dynamics (e.g. with stochastic volatility and long-memory) that there is an optimal threshold type strategy which can be learned. Subsequently, we numerically show the convergence of the algorithm. Furthermore, we deal with the typically problematic question of how to choose the hyperparameters (the parameters of the algorithm and not the dynamics of the prices) without knowing anything about the price other than a small sample.

Suggested Citation

  • Zsolt Nika & Mikl'os R'asonyi, 2019. "Learning Threshold-Type Investment Strategies with Stochastic Gradient Method," Papers 1907.02457, arXiv.org.
    • Handle: RePEc:arx:papers:1907.02457
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    References listed on IDEAS

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    1. G. Yin & Q. Zhang & F. Liu & R. H. Liu & Y. Cheng, 2006. "Stock Liquidation Via Stochastic Approximation Using Nasdaq Daily And Intra‐Day Data," Mathematical Finance, Wiley Blackwell, vol. 16(1), pages 217-236, January.
    2. Laruelle Sophie & Pagès Gilles, 2012. "Stochastic approximation with averaging innovation applied to Finance," Monte Carlo Methods and Applications, De Gruyter, vol. 18(1), pages 1-51, January.
    3. R. Cont, 2001. "Empirical properties of asset returns: stylized facts and statistical issues," Quantitative Finance, Taylor & Francis Journals, vol. 1(2), pages 223-236.
    4. Zsolt Nika & Miklos Rásonyi, 2018. "Log-Optimal Portfolios with Memory Effect," Applied Mathematical Finance, Taylor & Francis Journals, vol. 25(5-6), pages 557-585, November.
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