Asset Pricing with Stochastic Differential Utility

Abstract

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. Article published by Oxford University Press on behalf of the Society for Financial Studies in its journal, The Review of Financial Studies.