Asset pricing with time preference shocks: Existence and uniqueness

This paper studies existence and uniqueness of recursive utility in asset pricing models with time preference shocks. We provide conditions that clarify existence and uniqueness for a wide range of models, including exact necessary and sufficient conditions for standard formulations. The conditions isolate the roles of preference parameters, as well as the different risks that drive the consumption and preference shock processes. By deriving and decomposing a stability coefficient for recursive utility models, we show how different parameters in the model interact to determine existence and uniqueness of solutions.