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Asset Prices in an Exchange Economy with Habit Formation
Jerome B. Detemple
Fernando Zapatero
Abstract
This paper analyzes asset prices in an exchange economy in which the preferences of the representative agent exhibit habit formation. For a general class of utility indices and endowment processes we (i) characterize the optimal demand for consumption, and (ii) derive closed form solutions for the interest rate and the excess return on risky assets. Our analysis demonstrates that consumption smoothness may obtain even when the interest rate is stochastic. In economies with habit formation the consumption CAPM need not hold when the coefficients of the endowment process are stochastic processes; asset risk premia are larger under mild assumptions. The interest rate depends on the growth in the standard of living. Historical consumption as well as possible future consumption paths are determinants of the current interest rate. The analysis provides new testable restrictions on the behavior of financial assets. A new methodology, Malliavin calculus, is introduced to compute equilibrium asset risk premia.
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