Journal Of The Econometric Society

An International Society for the Advancement of Economic
Theory in its Relation to Statistics and Mathematics

Edited by: Guido W. Imbens • Print ISSN: 0012-9682 • Online ISSN: 1468-0262

Econometrica: Mar, 1992, Volume 60, Issue 2

Stochastic Differential Utility<353:SDU>2.0.CO;2-9
p. 353-394

Darrell Duffie, Larry G. Epstein

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.

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