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Rev Fin 1992; 5:411-436
© 1992 the Society for Financial Studies
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Asset pricing with stochastic differential utility
1 Graduate School of Business, Stanford University, Stanford, CA 94305-5015, USA
2 University of Toronto, Canada
z Corresponding author
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.
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