Causal analysis of extreme risk in a network of industry portfolios

We provide a comprehensive review of causal dependence through a max-linear structural equation model. Such models express each node variable as a max-linear function of its parental node variables in a directed acyclic graph and some exogenous innovation. We reformulate results on structure learning and estimation, which we apply to a network of financial data. A new method, based on hard-thresholding and on the Hamming distance, estimates a sparse DAG for extreme risk~propagation.