Uniqueness of Recursive Utility with Unbounded Consumption and Non-Expected Utility

Abstract: We derive sufficient conditions for the existence, non-existence, uniqueness and global attractivity of stochastic recursive utilities. Our approach uses abstract order-theoretic fixed-point arguments, allowing us to accommodate a large class of Markov consumption-growth models with unbounded per-period consumption and a broad range of recursive preferences, including non-expected utility specifications. We illustrate the usefulness of the framework through macro-finance applications to widely used consumption-growth models under several preference specifications, including Epstein--Zin preferences, multiple priors, smooth ambiguity, and Hansen--Sargent robust-control preferences. In each application, our general conditions reduce to a simple, economically interpretable parameter test that shows how fundamental parameters influence existence and uniqueness. While uniqueness of recursive utility can be difficult to guarantee in unbounded environments, in a Markov setting with non-unit elasticity we establish uniqueness within the class of recursive utilities having a so-called separability property.