Dynamic Mean-Variance Model with Borrowing Constraint under the Constant Elasticity of Variance Process
This paper studies a continuous-time dynamic mean-variance portfolio selection problem with the constraint of a higher borrowing rate, in which stock price is governed by a constant elasticity of variance (CEV) process. Firstly, we apply Lagrange duality theorem to change an original mean-variance p...
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2013/348059 |
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| _version_ | 1832558161622466560 |
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| author | Hao Chang Xi-min Rong |
| author_facet | Hao Chang Xi-min Rong |
| author_sort | Hao Chang |
| collection | DOAJ |
| description | This paper studies a continuous-time dynamic mean-variance portfolio selection problem with the constraint of a higher borrowing rate, in which stock price is governed by a constant elasticity of variance (CEV)
process. Firstly, we apply Lagrange duality theorem to change an original mean-variance problem into an equivalent optimization one. Secondly, we use dynamic programming principle to get the Hamilton-Jacobi-Bellman
(HJB) equation for the value function, which is a more sophisticated nonlinear second-order partial differential
equation. Furthermore, we use Legendre transform and dual theory to transform the HJB equation into its dual one.
Finally, the closed-form solutions to the optimal investment strategy and efficient frontier are derived by applying
variable change technique. |
| format | Article |
| id | doaj-art-2dc5e5981d3f4dbf8391f5ca71652a14 |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-2dc5e5981d3f4dbf8391f5ca71652a142025-02-03T01:33:05ZengWileyJournal of Applied Mathematics1110-757X1687-00422013-01-01201310.1155/2013/348059348059Dynamic Mean-Variance Model with Borrowing Constraint under the Constant Elasticity of Variance ProcessHao Chang0Xi-min Rong1Department of Mathematics, Tianjin Polytechnic University, Tianjin 300387, ChinaSchool of Science, Tianjin University, Tianjin 300072, ChinaThis paper studies a continuous-time dynamic mean-variance portfolio selection problem with the constraint of a higher borrowing rate, in which stock price is governed by a constant elasticity of variance (CEV) process. Firstly, we apply Lagrange duality theorem to change an original mean-variance problem into an equivalent optimization one. Secondly, we use dynamic programming principle to get the Hamilton-Jacobi-Bellman (HJB) equation for the value function, which is a more sophisticated nonlinear second-order partial differential equation. Furthermore, we use Legendre transform and dual theory to transform the HJB equation into its dual one. Finally, the closed-form solutions to the optimal investment strategy and efficient frontier are derived by applying variable change technique.http://dx.doi.org/10.1155/2013/348059 |
| spellingShingle | Hao Chang Xi-min Rong Dynamic Mean-Variance Model with Borrowing Constraint under the Constant Elasticity of Variance Process Journal of Applied Mathematics |
| title | Dynamic Mean-Variance Model with Borrowing Constraint under the Constant Elasticity of Variance Process |
| title_full | Dynamic Mean-Variance Model with Borrowing Constraint under the Constant Elasticity of Variance Process |
| title_fullStr | Dynamic Mean-Variance Model with Borrowing Constraint under the Constant Elasticity of Variance Process |
| title_full_unstemmed | Dynamic Mean-Variance Model with Borrowing Constraint under the Constant Elasticity of Variance Process |
| title_short | Dynamic Mean-Variance Model with Borrowing Constraint under the Constant Elasticity of Variance Process |
| title_sort | dynamic mean variance model with borrowing constraint under the constant elasticity of variance process |
| url | http://dx.doi.org/10.1155/2013/348059 |
| work_keys_str_mv | AT haochang dynamicmeanvariancemodelwithborrowingconstraintundertheconstantelasticityofvarianceprocess AT ximinrong dynamicmeanvariancemodelwithborrowingconstraintundertheconstantelasticityofvarianceprocess |