Existence of competitive equilibria for option markets (Q1262190)

In a general equilibrium model with options, \textit{H. Polemarchakis} and \textit{Bon-Il Ku} [``Options and equilibrium'', Working Paper, Columbia University (1986)] give an example of an economy where no competitive equilibrium exists. Their model is robust in the sense that slight changes of the parameters of the economy do not lead to the existence of an equilibrium. The aim of this paper is to show that this non-existence of equilibrium results from too little variation of the aggregate supply of commodities over the states of the world. We show that the fraction of economies (parameterized by endowments) with equilibria converges to one with increasing variation in the total endowment, in a precise sense.