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

Md. Azizul Baten | Zendy; Anton Abdulbasah Kamil | Zendy

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

Author(s) -

Md. Azizul Baten,

Anton Abdulbasah Kamil

Publication year - 2013

Publication title -

international journal of mathematics and mathematical sciences

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.21

H-Index - 39

eISSN - 1687-0425

pISSN - 0161-1712

DOI - 10.1155/2013/684757

Subject(s) - hamilton–jacobi–bellman equation , mathematics , viscosity solution , cobb–douglas production function , bellman equation , dimension (graph theory) , consumption (sociology) , mathematical economics , production (economics) , mathematical optimization , economics , pure mathematics , social science , sociology , macroeconomics

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

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