Optimal Consumption of a Divisible Durable Good

Rodney L. White Center for Financial Research Working Paper No. 020-98

Posted: 22 Oct 1998

See all articles by Hong Liu

Hong Liu

Washington University in St. Louis - Olin Business School; Fudan University - China Institute of Economics and Finance

Domenico Cuoco

University of Pennsylvania - Finance Department

Abstract

We examine the intertemporal optimal consumption and investment problem in a continuous-time economy with a divisible durable good. Consumption services are assumed to be proportional to the stock of the good held and adjustment of the stock is costly, in that it involves the payment of a proportional transaction cost. For the case in which the investor has an isoelastic utility function and asset prices follow a geometric Brownian motion, we establish the existence of an optimal policy and provide an explicit representation for the value function. We show that the investor acts so as to maintain the ratio of the stock of the durable to total wealth in a fixed (nonstochastic) range and that the optimal investment policy involves stochastic portfolio weights. The dependence of the optimal policies on the parameters of the model is also discussed.

JEL Classification: E21, E22, G12

Suggested Citation

Liu, Hong and Cuoco, Domenico, Optimal Consumption of a Divisible Durable Good. Rodney L. White Center for Financial Research Working Paper No. 020-98. Available at SSRN: https://ssrn.com/abstract=133488

Hong Liu

Washington University in St. Louis - Olin Business School ( email )

One Brookings Drive
Campus Box 1133
St. Louis, MO 63130-4899
United States
314-935-5883 (Phone)

Fudan University - China Institute of Economics and Finance ( email )

China

Domenico Cuoco (Contact Author)

University of Pennsylvania - Finance Department ( email )

The Wharton School
3620 Locust Walk
Philadelphia, PA 19104
United States

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