Existence and Uniqueness of Recursive Equilibria With Aggregate and Idiosyncratic Risk

59 Pages Posted: 10 Oct 2018 Last revised: 19 Sep 2023

See all articles by Elisabeth Proehl

Elisabeth Proehl

University of Amsterdam - Amsterdam School of Economics (ASE); Tinbergen Institute

Date Written: September 19, 2023

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.

Keywords: Existence, Uniqueness, Dynamic stochastic general equilibrium, Incomplete markets, Heterogeneous agents, Aggregate uncertainty, Convergence

JEL Classification: C61, C62, D51, D52, E21

Suggested Citation

Pröhl, Elisabeth, Existence and Uniqueness of Recursive Equilibria With Aggregate and Idiosyncratic Risk (September 19, 2023). Available at SSRN: https://ssrn.com/abstract=3250651 or http://dx.doi.org/10.2139/ssrn.3250651

Elisabeth Pröhl (Contact Author)

University of Amsterdam - Amsterdam School of Economics (ASE) ( email )

Roetersstraat 11
Amsterdam, North Holland 1018 WB
Netherlands

Tinbergen Institute ( email )

Burg. Oudlaan 50
Rotterdam, 3062 PA
Netherlands

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