Variational formulation for a general dynamic financial equilibrium problem: Balance law and liability formula

An evolutionary model for a multi-sector, multi-instrument financial equilibrium problem, with a general utility function, different prices for assets and liabilities and including the expenses for the management of the financial institutions is presented. In this general case, we give the evolutionary financial equilibrium conditions and prove their equivalence with an evolutionary variational inequality, from which existence results of the financial equilibrium follow. Moreover, making use of new nonlinear analysis results, we develop a Lagrange theory which allows one to study the behaviour of the financial equilibrium by means of the Lagrange multipliers. As a product of this analysis, we prove that for the financial model an equilibrium law together with a liability formula must be fulfilled, from which the reorganization of the existing financial disequilibrium depends.