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Rev Fin 2002; 15:1189-1221
© 2002 the Society for Financial Studies
An Isomorphism Between Asset Pricing Models With and Without Linear Habit Formation
Michigan State University
Northwestern University
Address correspondence to Costis Skiadas, Department of Finance, J. L. Kellogg Graduate School of Management, Northwestern University, 2001 Sheridan Rd., Evanston, IL 60208, or e-mail: c-skiadas{at}nwu.edu.
Abstract
We show an isomorphism between optimal portfolio selection or competitive equilibrium models with utilities incorporating linear habit formation, and corresponding models without habit formation. The isomorphism can be used to mechanically transform known solutions not involving habit formation to corresponding solutions with habit formation. For example, the Constantinides (1990) and Ingersoll (1992) solutions are mechanically obtained from the familiar Merton solutions for the additive utility case, without recourse to a Bellman equation or first-order conditions. More generally, recent solutions to portfolio selection problems with recursive utility and a stochastic investment opportunity set are readily transformed to novel solutions of corresponding problems with utility that combines recursivity with habit formation. The methodology also applies in the context of Hindy–Huang–Kreps (1992) preferences, where our isomorphism shows that the solution obtained by Hindy and Huang (1993) can be mechanically transformed to Dybvig's (1995) solution to the optimal consumption-investment problem with consumption ratcheting.