Optimal Investment-Consumption Problem with Constraint
In this paper, we consider an optimal investment-consumption problem subject to a closed convex constraint. In the problem, a constraint is imposed on both the investment and the consumption strategy, rather than just on the investment. The existence of solution is established by using the Martingal...
| Main Authors: | , , |
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| Format: | Journal Article |
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American Institute of Mathematical Sciences
2013
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| Online Access: | http://hdl.handle.net/20.500.11937/22554 |
| _version_ | 1848750902527131648 |
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| author | Liu, Jingzhen Yiu, Ka Fai Teo, Kok Lay (ah Nge) |
| author_facet | Liu, Jingzhen Yiu, Ka Fai Teo, Kok Lay (ah Nge) |
| author_sort | Liu, Jingzhen |
| building | Curtin Institutional Repository |
| collection | Online Access |
| description | In this paper, we consider an optimal investment-consumption problem subject to a closed convex constraint. In the problem, a constraint is imposed on both the investment and the consumption strategy, rather than just on the investment. The existence of solution is established by using the Martingale technique and convex duality. In addition to investment, our technique embeds also the consumption into a family of fictitious markets. However, with the addition of consumption, it leads to nonreflexive dual spaces. This difficulty is overcome by employing the so-called technique of \relaxation-projection" to establish the existence of solution to the problem. Furthermore, if the solution to the dual problem is obtained, then the solution to the primal problem can be found by using the characterization of the solution. An illustrative example is given with a dynamic risk constraint to demonstrate the method. |
| first_indexed | 2025-11-14T07:44:13Z |
| format | Journal Article |
| id | curtin-20.500.11937-22554 |
| institution | Curtin University Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-14T07:44:13Z |
| publishDate | 2013 |
| publisher | American Institute of Mathematical Sciences |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | curtin-20.500.11937-225542017-09-13T13:58:22Z Optimal Investment-Consumption Problem with Constraint Liu, Jingzhen Yiu, Ka Fai Teo, Kok Lay (ah Nge) dynamic risk constraint consumption duality martingale Investment In this paper, we consider an optimal investment-consumption problem subject to a closed convex constraint. In the problem, a constraint is imposed on both the investment and the consumption strategy, rather than just on the investment. The existence of solution is established by using the Martingale technique and convex duality. In addition to investment, our technique embeds also the consumption into a family of fictitious markets. However, with the addition of consumption, it leads to nonreflexive dual spaces. This difficulty is overcome by employing the so-called technique of \relaxation-projection" to establish the existence of solution to the problem. Furthermore, if the solution to the dual problem is obtained, then the solution to the primal problem can be found by using the characterization of the solution. An illustrative example is given with a dynamic risk constraint to demonstrate the method. 2013 Journal Article http://hdl.handle.net/20.500.11937/22554 10.3934/jimo.2013.9.743 American Institute of Mathematical Sciences fulltext |
| spellingShingle | dynamic risk constraint consumption duality martingale Investment Liu, Jingzhen Yiu, Ka Fai Teo, Kok Lay (ah Nge) Optimal Investment-Consumption Problem with Constraint |
| title | Optimal Investment-Consumption Problem with Constraint |
| title_full | Optimal Investment-Consumption Problem with Constraint |
| title_fullStr | Optimal Investment-Consumption Problem with Constraint |
| title_full_unstemmed | Optimal Investment-Consumption Problem with Constraint |
| title_short | Optimal Investment-Consumption Problem with Constraint |
| title_sort | optimal investment-consumption problem with constraint |
| topic | dynamic risk constraint consumption duality martingale Investment |
| url | http://hdl.handle.net/20.500.11937/22554 |