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

Abstract

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.

The convergence of the core of a fuzzy exchange economy

“…In other words, we came to the same concepts and results in this paper as Debreu and Scarf [6] when the FXE degenerates into the pure exchange economy. Finally, future work can be carried out to determine if good results could be generalized by considering different economic models with fuzzy preferences, such as the restricted participation on financial markets proposed by Donato et al [10] and the abstract economy studied by Rim and Kim [19].…”

“…Bi (p) = Bi (λp) and the link between P and P is as (11). In addition, the maximization problem (3) with constraint conditions (4) ( 5) is equivalent to the maximization problem (7) with the constraint conditions ( 8) and (10). Finally, it is true that the maximization problem (3) has a solution x * i (p) for each p ∈ P , denoted by x *…”