Optimal Consumption and Portfolio Rules with Durability and Habit Formation

Posted: 1 Nov 2000

See all articles by Ayman Hindy

Ayman Hindy

Independent

Steven H. Zhu

Banc of America Merrill Lynch; Morgan Stanley

Chi-fu Huang

Long Term Capital Management

Date Written: June 1993

Abstract

We study a model of consumption choice and portfolio allocation that captures, in two different interpretations, the combined effect of local substitution and habit formation and the combined effect of durability of consumption goods and habit formation over service flows from those goods. In a third interpretation, the model captures the idea of a dual purpose commodity. The optimal allocation problem is from the class of free boundary singular control problems. We discuss, formally, necessary, and sufficient conditions for a consumption and portfolio policy to be optimal. We also introduce a numerical technique based on approximating the original program by a sequence of discrete parameter Markov chain control problems. We provide convergence results of the value function, the optimal investment policy, and the optimal consumption regions in the approximating discrete control problems to those in the original continuous time dynamic program. We construct numerically the consumption boundary that divides the state space into two regions--one of immediate consumption and the other of abstinence. We show that both the wealth required to start consuming and the optimal fraction of wealth invested in the risky asset are cyclical functions in both the stock of the durable good and the standard of living. This is due to the interaction between the durability and habit formation effects. We also study the effect of the cyclical investment behavior on the equilibrium risk premium in a representative consumer economy.

JEL Classification: G11

Suggested Citation

Hindy, Ayman and Zhu, Steven H. and Huang, Chi-fu, Optimal Consumption and Portfolio Rules with Durability and Habit Formation (June 1993). Available at SSRN: https://ssrn.com/abstract=5978

Ayman Hindy (Contact Author)

Independent

No Address Available

Steven H. Zhu

Banc of America Merrill Lynch ( email )

Bank of America Plaza
335 Madison Ave, 5th Floor
New York, NY 10017
United States
646-855-1853 (Phone)

HOME PAGE: http://www.riskwhoswho.com/Charter-Members.html

Morgan Stanley ( email )

1585 Broadway
New York, NY 10036
United States

Chi-fu Huang

Long Term Capital Management

Greenwich, CT 06830
United States

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