Optimal auditing in the banking industry
Article first published online: 8 OCT 2007
Copyright © 2007 John Wiley & Sons, Ltd.
Optimal Control Applications and Methods
Volume 29, Issue 2, pages 127–158, March/April 2008
How to Cite
Bosch, T., Mukuddem-Petersen, J., Petersen, M. A. and Schoeman, I. (2008), Optimal auditing in the banking industry. Optim. Control Appl. Meth., 29: 127–158. doi: 10.1002/oca.828
- Issue published online: 26 MAR 2008
- Article first published online: 8 OCT 2007
- Manuscript Accepted: 27 AUG 2007
- Manuscript Revised: 18 JUN 2007
- Manuscript Received: 22 AUG 2006
- National Research Foundation. Grant Number: 2074218
- stochastic modeling and optimization;
- bank auditing
As a result of the new regulatory prescripts for banks, known as the Basel II Capital Accord, there has been a heightened interest in the auditing process. Our paper considers this issue with a particular emphasis on the auditing of reserves, assets and capital in both a random and non-random framework. The analysis relies on the stochastic dynamic modeling of banking items such as loans, reserves, Treasuries, outstanding debts, bank capital and government subsidies. In this regard, one of the main novelties of our contribution is the establishment of optimal bank reserves and a rate of depository consumption that is of importance during an (random) audit of the reserve requirements. Here the specific choice of a power utility function is made in order to obtain an analytic solution in a Lévy process setting. Furthermore, we provide explicit formulas for the shareholder default and regulator closure rules, for the case of a Poisson-distributed random audit. A property of these rules is that they define the standard for minimum capital adequacy in an implicit way. In addition, we solve an optimal auditing time problem for the Basel II capital adequacy requirement by making use of Lévy process-based models. This result provides information about the optimal timing of an internal audit when the ambient value of the capital adequacy ratio is taken into account and the bank is able to choose the time at which the audit takes place. Finally, we discuss some of the economic issues arising from the analysis of the stochastic dynamic models of banking items and the optimization procedure related to the auditing process. Copyright © 2007 John Wiley & Sons, Ltd.