Asset Pricing with Stochastic Differential Utility

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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.