International Journal of Mathematics and Mathematical Sciences
Volume 2013 (2013), Article ID 684757, 8 pages
http://dx.doi.org/10.1155/2013/684757
Research Article

Optimal Consumption in a Stochastic Ramsey Model with Cobb-Douglas Production Function

Md. Azizul Baten1 and Anton Abdulbasah Kamil2

1Department of Decision Science, School of Quantitative Sciences, Universiti Utara Malaysia (UUM), Sintok, 06010 Kedah, Malaysia
2Mathematics Program, School of Distance Education, Universiti Sains Malaysia (USM), 11800 Penang, Malaysia

Received 9 November 2012; Revised 7 January 2013; Accepted 16 January 2013

Academic Editor: Aloys Krieg

Copyright © 2013 Md. Azizul Baten and Anton Abdulbasah Kamil. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

A stochastic Ramsey model is studied with the Cobb-Douglas production function maximizing the expected discounted utility of consumption. We transformed the Hamilton-Jacobi-Bellman (HJB) equation associated with the stochastic Ramsey model so as to transform the dimension of the state space by changing the variables. By the viscosity solution method, we established the existence of viscosity solution of the transformed Hamilton-Jacobi-Bellman equation associated with this model. Finally, the optimal consumption policy is derived from the optimality conditions in the HJB equation.