Stochastic flow diagrams

Article type: Research Article

Authors: Calkin, Neil J.^a | López de Prado, Marcos^{b; c; *}

Affiliations: [a] Department of Mathematical Sciences, Clemson University, Clemson, SC, USA | [b] Senior Managing Director, Guggenheim Partners, New York, NY, USA | [c] Research Affiliate, Computational Research Division, Lawrence Berkeley National Laboratory, Berkeley, CA, USA

Correspondence: [*] Corresponding author: Marcos López de Prado, Guggenheim Partners, 330 Madison Ave., New York, NY 10017, USA. E-mail: marcos.lopezdeprado@guggenheimpartners.com; www.QuantResearch.info.

Abstract: We introduce Stochastic Flow Diagrams (SFDs), a new mathematical approach to represent complex dynamic systems into a single weighted digraph. This topological representation provides a way to visualize what otherwise would be a morass of equations in differences. SFDs model the propagation and reverberation that follows a shock. For example, reverberation explains how a shock to a financial system can initiate a sequence of events that lead to a crash long after the occurrence of the shock. SFDs can simulate systems in stable, steady or explosive state. SFDs add Topology to the Statistical and Econometric toolkit. We believe that SFDs will help policy makers, investors and researchers communicate and discuss better the complexity of dynamic systems.

Keywords: 90C35, 90B15, 05C21, 62P05, 37M10

Keywords: Time series, graph theory, topology, financial flows, macro trading

DOI: 10.3233/AF-140032

Journal: Algorithmic Finance, vol. 3, no. 1-2, pp. 21-42, 2014