Existence and Uniqueness of Recursive Equilibria With Aggregate and Idiosyncratic Risk

Abstract

In this paper, I study the existence and uniqueness of recursive equilibria in economies with aggregate and idiosyncratic risk. Rather than relying on compactness to establish existence, I exploit the monotonicity property of the equilibrium model and rely on arguments from convex analysis. This methodology does not only give rise to a convergent iterative procedure, but more strikingly, it also yields uniqueness. To illustrate my theoretical results, I establish sufficient conditions for the existence and uniqueness of solutions to the stochastic growth model as in Krusell and Smith (1998) and the heterogeneous-agent exchange economy as in Huggett (1993) with aggregate risk.