Stochastic Differential Utility

A stochastic differential formulation of recursive utility is given sufficient conditions 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-Bellman-Jacobi characterization of optimality. A companion paper explores the implications for asset prices. Copyright 1992 by The Econometric Society.