Journal of Applied Mathematics

Journal of Applied Mathematics / 2007 / Article

Research Article | Open Access

Volume 2007 |Article ID 029343 | https://doi.org/10.1155/2007/29343

J. Mukuddem-Petersen, M. A. Petersen, I. M. Schoeman, B. A. Tau, "Maximizing Banking Profit on a Random Time Interval", Journal of Applied Mathematics, vol. 2007, Article ID 029343, 22 pages, 2007. https://doi.org/10.1155/2007/29343

Maximizing Banking Profit on a Random Time Interval

Academic Editor: Ibrahim Sadek
Received02 Mar 2007
Accepted01 Apr 2007
Published03 Jun 2007

Abstract

We study the stochastic dynamics of banking items such as assets, capital, liabilities and profit. A consideration of these items leads to the formulation of a maximization problem that involves endogenous variables such as depository consumption, the value of the bank's investment in loans, and provisions for loan losses as control variates. A solution to the aforementioned problem enables us to maximize the expected utility of discounted depository consumption over a random time interval, [t,τ], and profit at terminal time τ. Here, the term depository consumption refers to the consumption of the bank's profits by the taking and holding of deposits. In particular, we determine an analytic solution for the associated Hamilton-Jacobi-Bellman (HJB) equation in the case where the utility functions are either of power, logarithmic, or exponential type. Furthermore, we analyze certain aspects of the banking model and optimization against the regulatory backdrop offered by the latest banking regulation in the form of the Basel II capital accord. In keeping with the main theme of our contribution, we simulate the financial indices return on equity and return on assets that are two measures of bank profitability.

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Copyright © 2007 J. Mukuddem-Petersen 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.


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