Asset Pricing with Stochastic Differential Utility

This paper presents asset pricing theory 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 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. The paper also introduces a new multi-commodity factor-return model, as well as an extension of the “usual” discounted expected value formula for asset prices._x000B_