Dynamic mode decomposition for financial trading strategies.

*(English)*Zbl 1400.91558Summary: We demonstrate the application of an algorithmic trading strategy based upon the recently developed dynamic mode decomposition on portfolios of financial data. The method is capable of characterizing complex dynamical systems, in this case financial market dynamics, in an equation-free manner by decomposing the state of the system into low-rank terms whose temporal coefficients in time are known. By extracting key temporal coherent structures (portfolios) in its sampling window, it provides a regression to a best fit linear dynamical system, allowing for a predictive assessment of the market dynamics and informing an investment strategy. The data-driven analytics capitalizes on stock market patterns, either real or perceived, to inform buy/sell/hold investment decisions. Critical to the method is an associated learning algorithm that optimizes the sampling and prediction windows of the algorithm by discovering trading hot-spots. The underlying mathematical structure of the algorithms is rooted in methods from nonlinear dynamical systems and shows that the decomposition is an effective mathematical tool for data-driven discovery of market patterns.

##### MSC:

91G10 | Portfolio theory |

37E99 | Low-dimensional dynamical systems |

37G99 | Local and nonlocal bifurcation theory for dynamical systems |

37L65 | Special approximation methods (nonlinear Galerkin, etc.) for infinite-dimensional dissipative dynamical systems |

##### Keywords:

dynamic mode decomposition; Koopman operator; dynamical systems; financial trading; equation-free##### Software:

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\textit{J. Mann} and \textit{J. N. Kutz}, Quant. Finance 16, No. 11, 1643--1655 (2016; Zbl 1400.91558)

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