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Federal Reserve Bank of Atlanta
FRB Atlanta Working Paper
Consumption and asset prices with homothetic recursive preferences
Mark Fisher
Christian Gilles

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.

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Mark Fisher & Christian Gilles, Consumption and asset prices with homothetic recursive preferences, Federal Reserve Bank of Atlanta, FRB Atlanta Working Paper 99-17, 1999.
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Keywords: Asset pricing ; Consumption (Economics) ; Interest rates ; Wealth
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