## Journal of Applied Mathematics

### Minimizing Banking Risk in a Lévy Process Setting

#### Abstract

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.

#### Article information

Source
J. Appl. Math., Volume 2007 (2007), Article ID 32824, 25 pages.

Dates
First available in Project Euclid: 5 July 2007

https://projecteuclid.org/euclid.jam/1183667201

Digital Object Identifier
doi:10.1155/2007/32824

Mathematical Reviews number (MathSciNet)
MR2317884

Zentralblatt MATH identifier
1157.91018

#### Citation

Gideon, F.; Mukuddem-Petersen, J.; Petersen, M. A. Minimizing Banking Risk in a Lévy Process Setting. J. Appl. Math. 2007 (2007), Article ID 32824, 25 pages. doi:10.1155/2007/32824. https://projecteuclid.org/euclid.jam/1183667201

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