We study the consumption and investment choice of an agent in a continuous-time economy with a riskless asset, several risky ΓΏnancial assets, and two consumption goods, namely a perishable and a durable good with an uncertain price evolution. Assuming lognormal prices and a multiplicatively separabl
Optimal consumption of a divisible durable good
β Scribed by Domenico Cuoco; Hong Liu
- Publisher
- Elsevier Science
- Year
- 2000
- Tongue
- English
- Weight
- 434 KB
- Volume
- 24
- Category
- Article
- ISSN
- 0165-1889
No coin nor oath required. For personal study only.
β¦ Synopsis
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 "xed (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.
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