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Title: Time to consensus in financial causality networks: A Von Neumman entropy approach to contagion Authors:  Lorenzo Frattarolo - Ca Foscari Venezia (Italy) [presenting]
Roberto Casarin - University Ca' Foscari of Venice (Italy)
Monica Billio - University of Venice (Italy)
Michele Costola - Ca' Foscari University of Venice (Italy)
Abstract: Time to consensus is the time a networked system needs to reach a condition in which all of its constituents have the same state and can be considered a measure of information and shock diffusion in the system. Extending results in literature, to directed networks, we show that in the classical consensus dynamics, Shannon entropy decreases, while for quantum case, the von Neumann entropy (VNE) is non-decreasing and that they are equivalent frameworks, in terms of dynamics. We propose to measure classical time to consensus by measuring the time an equivalent quantum system takes to maximize its VNE. The relevance of consensus dynamics of stock returns for financial contagion could be understood by considering the convergence of returns to a common negative-valued state and the implied dynamical increase of dependence, a standard signature of financial contagion. We use rolling Granger Causality to approximate the networked dynamics of returns, obtain, by the Sinkorn-Knopp decomposition, a doubly stochastic matrix (the adjacency matrix of the corresponding balanced network) and compute a parsimonious Birkoff Von Neumman decomposition of the latter. Permutation matrices and convex weights from the decomposition are then used to compute, the quantum evolution operator, maximal VNE and time to consensus. We investigate the relevance of those measures also as an early warning for financial contagion episodes.