This paper presents the evolution of the most recent mathematical models of general equilibrium, starting with the model of contingent commodities, through the sequential model with securities, even to the case of equilibrium with default and collateralized securities markets. To this end, we discuss on the main ideas regarding the application of microeconomic theory ofgeneral equilibrium to situations involving the exchange and resource allocation under conditions ofuncertainty. Then we present the conditions of general equilibrium when financial markets are incomplete. We make a critical evaluation ofassumptions for such models. Further, we introduce the discussion ofthe role ofdefault in market general equilibrium, and finally we discuss the effect of collateral for the general equilibrium. Given a selection ofeight important papers, the article examines the assumptions and mathematical behavioral models of each family and examines the main theorems that demonstrate whether or not the existence ofgeneral equilibrium in incomplete security markets with default and collateral. Still follows a classification of the assumptions underlying the set of theorems of general equilibrium shown in the literature considered.
