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Portfolio Optimization for Cointelated Pairs: SDEs vs. Machine Learning

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  • Babak Mahdavi-Damghani
  • Konul Mustafayeva
  • Stephen Roberts
  • Cristin Buescu

Abstract

With the recent rise of Machine Learning as a candidate to partially replace classic Financial Mathematics methodologies, we investigate the performances of both in solving the problem of dynamic portfolio optimization in continuous-time, finite-horizon setting for a portfolio of two assets that are intertwined. In Financial Mathematics approach we model the asset prices not via the common approaches used in pairs trading such as a high correlation or cointegration, but with the cointelation model that aims to reconcile both short-term risk and long-term equilibrium. We maximize the overall P&L with Financial Mathematics approach that dynamically switches between a mean-variance optimal strategy and a power utility maximizing strategy. We use a stochastic control formulation of the problem of power utility maximization and solve numerically the resulting HJB equation with the Deep Galerkin method. We turn to Machine Learning for the same P&L maximization problem and use clustering analysis to devise bands, combined with in-band optimization. Although this approach is model agnostic, results obtained with data simulated from the same cointelation model as FM give an edge to ML.

Suggested Citation

  • Babak Mahdavi-Damghani & Konul Mustafayeva & Stephen Roberts & Cristin Buescu, 2018. "Portfolio Optimization for Cointelated Pairs: SDEs vs. Machine Learning," Papers 1812.10183, arXiv.org, revised Oct 2019.
  • Handle: RePEc:arx:papers:1812.10183
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    File URL: http://arxiv.org/pdf/1812.10183
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    1. Jim Gatheral & Antoine Jacquier, 2014. "Arbitrage-free SVI volatility surfaces," Quantitative Finance, Taylor & Francis Journals, vol. 14(1), pages 59-71, January.
    2. John C. Cox & Jonathan E. Ingersoll Jr. & Stephen A. Ross, 2005. "A Theory Of The Term Structure Of Interest Rates," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.),Theory Of Valuation, chapter 5, pages 129-164, World Scientific Publishing Co. Pte. Ltd..
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