Functional inequalities, regularity and computation of the deficit and surplus variables in the financial equilibrium problem

This paper is concerned with a general model of financial flows and prices related to individual entities, called sectors, which invest in financial instruments as assets and as liabilities. In particular, using delicate tools of Functional Analysis, besides existence results of financial equilibrium, in the dual formulation, the Lagrange functions ${\rho }_j^{\ast 1}\left(t\right)$ and ${\rho }_j^{\ast 2}\left(t\right)$ , called ‘deficit’ and ‘surplus’ variables, appear and reveal to be very relevant in order to analyze the financial model and the possible insolvencies, which can lead to a financial contagion. In the paper the continuity of these Lagrange functions is proved. Finally, a procedure for the calculus of these variables is suggested.