Functional Inequalities and Analysis of Contagion in the Financial Networks

in very recent papers, using delicate tools of functional analysis, a general equilibrium models of Financial flows and prices is studied. In particular without
using a technical language, But using the universal language of mathematics, some
significant laws, as Deficit formula, Balance law and Liability formula for the man-
agement of the world economy are provided. Further a simple but useful economical
indicator E(t) is considered. In this paper, considering the Lagrange dual formulation of the financial model, the Lagrange variables called “deficit” and “surplus”
variables, are considered. By means of these variables we study the possible insolvencies related to the financial instruments and their propagation to the entire system, producing a “financial contagion”.