Restricted Participation on Financial Markets: A General Equilibrium Approach Using Variational Inequality Methods

We deal with the analysis of a general equilibrium model with restricted participation in financial markets and with numeraire assets. We consider an exchange economy and assume that there are two periods of time and S possible states of nature in the second period. Markets may in principle be complete, but each household has her own specific restricted way to access to it. In particular, we assume that households are allowed to choose portfolios in a closed and convex set containing zero. Our main goal in this work is to provide a proof of existence of equilibria under relatively general assumptions, by assuming that the households may have non-complete or non-transitive preferences, and by using a variational inequality approach. More precisely, we introduce a sequence of generalized quasi-variational inequalities and we show that an associated sequence of solutions converges to an equilibrium.