[Asset pricing theory is presented with representative-agent utility given by a stochastic differential formulation of recursive utility. Asset returns are characterized from general first-order conditions of the Hamilton-Bellman-Jacobi equation for optimal control. Homothetic representative-agent recursive utility functions are shown to imply that excess expected rates of return on securities are given by a linear combination of the continuous-time market-portfolio-based capital asset pricing model (CAPM) and the consumption-based CAPM. The Cox, Ingersoll, and Ross characterization of the term structure is examined with a recursive generalization, showing the response of the term structure to variations in risk aversion. Also, a new multicommodity factor-return model, as well as an extension of the "usual" discounted expected value formula for asset prices, is introduced.]

Asset pricing theory is presented with representative-agent utility given by a stochastic differential formulation of recursive utility. Asset returns are characterized from general first-order conditions of the Hamilton–Bellman–Jacobi equation for optimal control. Homothetic representative-agent recursive utility functions are shown to imply that excess expected rates of return on securities are given by a linear combination of the continuous-time market-portfolio-based capital asset pricing model (CAPM) and the consumption-based CAPM. The Cox, Ingersoll, and Ross characterization of the term structure is examined with a recursive generalization, showing the response of the term structure to variations in risk aversion. Also, a new multicommodity factor-return model, as well as an extension of the “usual” discounted expected value formula for asset prices, is introduced.

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.