Existence of financial equilibria with real assets: a variational inequality approach

This paper presents the analysis of the existence of equilibria in a two-period general equilibrium model with incomplete financial markets and real assets by means of a variational inequality approach. A definition of fictitious equilibrium is presented and it is shown to be equivalent to the definition of equilibrium under a suitable rank condition of the return matrix. Then the fictitious equilibrium is characterized in terms of a generalized quasi-variational inequality involving Grassmannian manifolds. The chosen variational inequality is constituted by two parts: the former one relates to the individuals’ maximization problems and the latter one exploits the market clearing conditions.