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Log-Optimal Portfolios with Memory Effect

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  • Zsolt Nika
  • Miklos Rásonyi

Abstract

In portfolio optimization a classical problem is to trade with assets so as to maximize some kind of utility of the investor. In our paper this problem is investigated for assets whose prices depend on their past values in a non-Markovian way. Such models incorporate several features of real price processes better than Markov processes do. Our utility function is the widespread logarithmic utility, the formulation of the model is discrete in time. Despite the problem being a well-known one, there are few results where memory is treated systematically in a parametric model. Our algorithm is optimal and this optimality is guaranteed for a rich class of model specifications. Moreover, the algorithm runs online, i.e., the optimal investment is achieved in a day-by-day manner, using simple numerical integration, without Monte-Carlo simulations. Theoretical results are demonstrated by numerical experiments as well.

Suggested Citation

  • 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.
    • Handle: RePEc:taf:apmtfi:v:25:y:2018:i:5-6:p:557-585
    DOI: 10.1080/1350486X.2018.1542323
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    Cited by:

    1. Zsolt Nika & Mikl'os R'asonyi, 2019. "Learning Threshold-Type Investment Strategies with Stochastic Gradient Method," Papers 1907.02457, arXiv.org.
    2. Michael Senescall & Rand Kwong Yew Low, 2024. "Quantitative Portfolio Management: Review and Outlook," Mathematics, MDPI, vol. 12(18), pages 1-25, September.

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