Journal of Applied Mathematics
Volume 2007 (2007), Article ID 32824, 25 pages
Research Article

Minimizing Banking Risk in a Lévy Process Setting

F. Gideon, J. Mukuddem-Petersen, and M. A. Petersen

Department of Mathematics and Applied Mathematics, Faculty of Science, North-West University (Potchefstroom Campus), Private Bag X 6001, Potchefstroom 2520, South Africa

Received 28 February 2007; Accepted 18 May 2007

Academic Editor: Ibrahim Sadek

Copyright © 2007 F. Gideon et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.