Existence Conditions for Asset Pricing Models with Recursive Utility

Abstract

Modern asset pricing models combine recursive preferences with complex dynamics for the underlying consumption process. Existence of solutions is, for many of these models, an unsettled question. This paper introduces a novel technique to prove existence and non-existence for models with recursive preferences. The approach applies to many models of interest, such as those with long-run consumption risks, with stochastic volatility and jumps, with volatility of volatility, with time-varying consumption disasters, and with smooth ambiguity aversion and learning. Collectively the proven results settle the existence question for many of today's leading asset pricing models.

Keywords: Asset pricing, existence, jumps, long-run risk, recursive utility

JEL Classification: G11, G12