Recursive Utility with Preference Shocks : Existence and Uniqueness

This paper studies existence and uniqueness of recursively defined utility in asset pricing models with preference shocks. We provide conditions that clarify existence and uniqueness for a wide range of models, including exact necessary and sufficient conditions for the most standard formulations. The conditions isolate the roles of preference parameters, as well as the different risks that drive the consumption and preference shock processes. One notable finding is that, for agents who prefer early resolution of risk, introducing preference shocks always relaxes the existence condition. This effect is large in common calibrations, so the presence of preference shocks makes the existence of a solution significantly more likely