Minimizing Banking Risk in a Lévy Process Setting
The primary functions of a bank are to obtain funds through deposits from external sources and to use the said funds to issue loans. Moreover, risk management practices related to the withdrawal of these bank deposits have always been of considerable interest. In this spirit, we construct Lévy proce...
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| Format: | Article |
| Language: | English |
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Wiley
2007-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2007/32824 |
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| author | F. Gideon J. Mukuddem-Petersen M. A. Petersen |
| author_facet | F. Gideon J. Mukuddem-Petersen M. A. Petersen |
| author_sort | F. Gideon |
| collection | DOAJ |
| description | The primary functions of a bank are to obtain funds through deposits from external sources and to use the said funds to issue loans. Moreover, risk management practices related to the withdrawal of these bank deposits have always been of considerable interest. In this spirit, we construct Lévy process-driven models of banking reserves in order to address the problem of hedging deposit withdrawals from such institutions by means of reserves. Here reserves are related to outstanding debt and acts as a proxy for the assets held by the bank. The aforementioned modeling enables us to formulate a stochastic optimal control problem related to the minimization of reserve, depository, and intrinsic risk that are associated with the reserve process, the net cash flows from depository activity, and cumulative costs of the bank's provisioning strategy, respectively. A discussion of the main risk management issues arising from the optimization problem mentioned earlier forms an integral part of our paper. This includes the presentation of a numerical example involving a simulation of the provisions made for deposit withdrawals via treasuries and reserves. |
| format | Article |
| id | doaj-art-04f6a36719064ae5b5c846d98e0c117f |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2007-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-04f6a36719064ae5b5c846d98e0c117f2025-02-03T01:07:53ZengWileyJournal of Applied Mathematics1110-757X1687-00422007-01-01200710.1155/2007/3282432824Minimizing Banking Risk in a Lévy Process SettingF. Gideon0J. Mukuddem-Petersen1M. A. Petersen2Department of Mathematics and Applied Mathematics, Faculty of Science, North-West University (Potchefstroom Campus), Private Bag X 6001, Potchefstroom 2520, South AfricaDepartment of Mathematics and Applied Mathematics, Faculty of Science, North-West University (Potchefstroom Campus), Private Bag X 6001, Potchefstroom 2520, South AfricaDepartment of Mathematics and Applied Mathematics, Faculty of Science, North-West University (Potchefstroom Campus), Private Bag X 6001, Potchefstroom 2520, South AfricaThe primary functions of a bank are to obtain funds through deposits from external sources and to use the said funds to issue loans. Moreover, risk management practices related to the withdrawal of these bank deposits have always been of considerable interest. In this spirit, we construct Lévy process-driven models of banking reserves in order to address the problem of hedging deposit withdrawals from such institutions by means of reserves. Here reserves are related to outstanding debt and acts as a proxy for the assets held by the bank. The aforementioned modeling enables us to formulate a stochastic optimal control problem related to the minimization of reserve, depository, and intrinsic risk that are associated with the reserve process, the net cash flows from depository activity, and cumulative costs of the bank's provisioning strategy, respectively. A discussion of the main risk management issues arising from the optimization problem mentioned earlier forms an integral part of our paper. This includes the presentation of a numerical example involving a simulation of the provisions made for deposit withdrawals via treasuries and reserves.http://dx.doi.org/10.1155/2007/32824 |
| spellingShingle | F. Gideon J. Mukuddem-Petersen M. A. Petersen Minimizing Banking Risk in a Lévy Process Setting Journal of Applied Mathematics |
| title | Minimizing Banking Risk in a Lévy Process Setting |
| title_full | Minimizing Banking Risk in a Lévy Process Setting |
| title_fullStr | Minimizing Banking Risk in a Lévy Process Setting |
| title_full_unstemmed | Minimizing Banking Risk in a Lévy Process Setting |
| title_short | Minimizing Banking Risk in a Lévy Process Setting |
| title_sort | minimizing banking risk in a levy process setting |
| url | http://dx.doi.org/10.1155/2007/32824 |
| work_keys_str_mv | AT fgideon minimizingbankingriskinalevyprocesssetting AT jmukuddempetersen minimizingbankingriskinalevyprocesssetting AT mapetersen minimizingbankingriskinalevyprocesssetting |