The 
 copyright 
 to 
 this 
 article 
 is 
 held 
 by 
 the 


It may be downloaded, printed and reproduced only for personal or classroom use. Absolutely no downloading or copying may be done for, or on behalf of, any for‐profit commercial firm or other commercial purpose without the explicit permission of the Econometric Society. For this purpose, contact Claire Sashi, General Manager, at [email protected]. This paper presents a stochastic differential formulation of recursive utility. Sufficient conditions are given for existence, uniqueness, time consistency, monotonicity, continuity, risk aversion, concavity, and other properties. In the setting of Brownian information, recursive and intertemporal expected utility functions are observationally distinguishable. However, one cannot distinguish between a number of non-expected-utility theories of one-shot choice under uncertainty after they are suitably integrated into an intertemporal framework. In a "smooth" Markov setting, the stochastic differential utility model produces a generalization of the Hamilton-Jacobi-Bellman characterization of optimality. A companion paper explores the implications for asset prices.