A stochastic control model of investment, production and consumption

Fleming, Wendell; Pang, Tao

doi:10.1090/S0033-569X-04-00941-1

Authors: Wendell H. Fleming and Tao Pang
Journal: Quart. Appl. Math. 63 (2005), 71-87
MSC (2000): Primary 60H30, 91B28, 93E20
DOI: https://doi.org/10.1090/S0033-569X-04-00941-1
Published electronically: December 17, 2004
MathSciNet review: 2126570
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Abstract: We consider a stochastic control model in which an economic unit has productive capital and also liabilities in the form of debt. The worth of capital changes over time through investment as well as through random Brownian fluctuations in the unit price of capital. Income from production is also subject to random Brownian fluctuations. The goal is to choose investment and consumption controls which maximize total expected discounted HARA utility of consumption. Optimal control policies are found using the method of dynamic programming. In case of logarithmic utility, these policies have explicit forms.

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