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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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2013/684757 |
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| author | Md. Azizul Baten Anton Abdulbasah Kamil |
| author_facet | Md. Azizul Baten Anton Abdulbasah Kamil |
| author_sort | Md. Azizul Baten |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-6974445943ad427fafa594a6235dbb02 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-6974445943ad427fafa594a6235dbb022025-02-03T07:24:19ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252013-01-01201310.1155/2013/684757684757Optimal Consumption in a Stochastic Ramsey Model with Cobb-Douglas Production FunctionMd. Azizul Baten0Anton Abdulbasah Kamil1Department of Decision Science, School of Quantitative Sciences, Universiti Utara Malaysia (UUM), Sintok, 06010 Kedah, MalaysiaMathematics Program, School of Distance Education, Universiti Sains Malaysia (USM), 11800 Penang, MalaysiaA 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.http://dx.doi.org/10.1155/2013/684757 |
| spellingShingle | Md. Azizul Baten Anton Abdulbasah Kamil Optimal Consumption in a Stochastic Ramsey Model with Cobb-Douglas Production Function International Journal of Mathematics and Mathematical Sciences |
| title | Optimal Consumption in a Stochastic Ramsey Model with Cobb-Douglas Production Function |
| title_full | Optimal Consumption in a Stochastic Ramsey Model with Cobb-Douglas Production Function |
| title_fullStr | Optimal Consumption in a Stochastic Ramsey Model with Cobb-Douglas Production Function |
| title_full_unstemmed | Optimal Consumption in a Stochastic Ramsey Model with Cobb-Douglas Production Function |
| title_short | Optimal Consumption in a Stochastic Ramsey Model with Cobb-Douglas Production Function |
| title_sort | optimal consumption in a stochastic ramsey model with cobb douglas production function |
| url | http://dx.doi.org/10.1155/2013/684757 |
| work_keys_str_mv | AT mdazizulbaten optimalconsumptioninastochasticramseymodelwithcobbdouglasproductionfunction AT antonabdulbasahkamil optimalconsumptioninastochasticramseymodelwithcobbdouglasproductionfunction |