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

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 chang...

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Bibliographic Details
Published in:International Journal of Mathematics and Mathematical Sciences 2013, Vol.2013 (2013), p.206-213
Main Authors: Baten, Md. Azizul, Kamil, Anton Abdulbasah
Format: Article
Language:English
Subjects:
Economic research
Financial management
Learning models (Stochastic processes)
Mathematical analysis
Mathematical models
Mathematical research
Optimization
Policies
Stochasticity
Transforms
Utilities
Viscosity
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Summary: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.
ISSN:0161-1712
1687-0425
DOI:10.1155/2013/684757