Convergence of the equilibrium prices in a family of financial models

In this paper, we consider a family of complete or incomplete Financial models such that the price processes of the Financial assets converge in distribution to those in a limit model. Different authors pointed out that we do not have necessarily convergence of the arbitrage pricing intervals in that context. We prove here that we have very good convergence properties for the equilibrium pricing interval as defined by Bizid, Jouini and Koehl (1998) in discrete time or Jouini and Napp (1999) in continuous time.