Consumption and Asset Prices with Homothetic Recursive Preferences

Mark Fisher and Christian Gilles
Federal Reserve Bank of Atlanta
Working Paper 99-17
November 1999

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When preferences are homothetic, utility can be expressed in terms of current consumption and a variable that captures all information about future opportunities. We use this observation to express the differential equation that characterizes utility as a restriction on the information variable in terms of the dynamics of consumption. We derive the supporting price system and returns process and thereby characterize optimal consumption and portfolio decisions. We provide a fast and accurate numerical solution method and illustrate its use with a number of Markovian models. In addition, we provide insight by changing the numeraire from units of consumption to units of the consumption process. In terms of the new units, the wealth-consumption ratio (which is closely related to the information variable) is the value of a coupon bond and the existence of an infinite-horizon solution depends on the positivity of the asymptotic forward rate.

JEL classification: G12

Key words: recursive preferences, stochastic differential utility, general equilibrium, optimal consumption, optimal portfolio, equity premium, term structure of interest rates, asset pricing

This paper is a substantially revised version of "Consumption and Asset Prices with Recursive Preferences" that appeared as a Federal Reserve Board working paper (FEDS 98-40). The authors thank Greg Duffee and Costis Skiadas for useful conversations. The views expressed here are the authors' and not necessarily those of the Federal Reserve Bank of Atlanta, the Federal Reserve System, or Bear Stearns & Co. Any remaining errors are the authors' responsibility.

Please address questions regarding content to Mark Fisher, Senior Economist, Research Department, Federal Reserve Bank of Atlanta, 104 Marietta Street, NW, Atlanta, Georgia 30303-2713, 404/498-8757,; or Christian Gilles, Managing Director, FAST Group, 5th Floor, Bear, Stearns & Co., 245 Park Avenue, New York, New York 10167, 212/272-3446,