Ambiguity Aversion and Incompleteness of Financial Markets

We consider a stylized bond-equity economy, which though incomplete per se, has a rich enough set of assets available for trade such that given standard assumptions about behavior under uncertainty, the equilibrium allocation would arbitrarily approximate a complete market allocation. We show, however, that when agents' beliefs are given by a set of probabilities and agents are ambiguity averse, a certain subset of the available assets will not be actually traded in equilibrium, given "sufficient" ambiguity aversion. What determines an asset's vulnerability to ambiguity aversion is whether its payoffs have an idiosyncratic component. If, (1) the range of variation of the payoff's idiosyncratic component is "large" relative to the range of the variation of the component correlated with the endowment vector and, (2) the ambiguity of the agents' common belief about the idiosyncratic component is sufficiently high, then the asset will not be traded in any general equilibrium of the finance economy. Moreover, we also find that the effect of idiosyncracy cannot simply be "washed away" by the standard techniques of diversification relying on the laws of large numbers, as it would be if the agents' beliefs were not ambiguous.