Journal of Applied Mathematics
Volume 2007 (2007), Article ID 29343, 22 pages
doi:10.1155/2007/29343
Research Article

Maximizing Banking Profit on a Random Time Interval

1Department of Mathematics and Applied Mathematics, Faculty of Science, North-West University (Potchefstroom Campus), Private Bag X 6001, Potchefstroom 2520, South Africa
2School of Modeling Sciences, North-West University (Vaaldriehoek Campus), Private Bag X 6001, P.O. Box 1174, Vanderbijlpark 1900, South Africa

Received 2 March 2007; Accepted 1 April 2007

Academic Editor: Ibrahim Sadek

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.

Linked References

  1. Basel Committee on Banking Supervision, “The New Basel Capital Accord,” 2001, Bank for International Settlements, http://www.bis.org/publ/bcbsca.htm.
  2. Basel Committee on Banking Supervision, “International Convergence of Capital Measurement and Capital Standards; A Revised Framework,” June 2004, Bank for International Settlements, http://www.bis.org/publ/bcbs107.pdf.
  3. F. Modigliani and M. H. Miller, “The cost of capital, corporation finance and the theory of investment,” The American Economic Review, vol. 48, no. 3, pp. 261–297, 1958.
  4. A. N. Berger, R. J. Herring, and G. P. Szegö, “The role of capital in financial institutions,” Journal of Banking & Finance, vol. 19, no. 3-4, pp. 393–430, 1995. View at Publisher · View at Google Scholar
  5. D. W. Diamond and R. G. Rajan, “A theory of bank capital,” The Journal of Finance, vol. 55, no. 6, pp. 2431–2465, 2000. View at Publisher · View at Google Scholar
  6. H. E. Leland, “Corporate debt value, bond covenants, and optimal capital structure,” The Journal of Finance, vol. 49, no. 4, pp. 1213–1252, 1994. View at Publisher · View at Google Scholar
  7. J.-C. Rochet, “Capital requirements and the behaviour of commercial banks,” European Economic Review, vol. 36, no. 5, pp. 1137–1170, 1992. View at Publisher · View at Google Scholar
  8. T. Dangl and J. Zechner, “Credit risk and dynamic capital structure choice,” Journal of Financial Intermediation, vol. 13, no. 2, pp. 183–204, 2004. View at Publisher · View at Google Scholar
  9. J.-P. Decamps, J.-C. Rochet, and B. Roger, “The three pillars of Basel II: optimizing the mix,” Journal of Financial Intermediation, vol. 13, no. 2, pp. 132–155, 2004. View at Publisher · View at Google Scholar
  10. M. A. Petersen and J. Mukuddem-Petersen, “Stochastic behaviour of risk-weighted bank assets under the Basel II capital accord,” Applied Financial Economics Letters, vol. 1, no. 3, pp. 133–138, 2005. View at Publisher · View at Google Scholar
  11. R. Repullo, “Capital requirements, market power, and risk-taking in banking,” Journal of Financial Intermediation, vol. 13, no. 2, pp. 156–182, 2004. View at Publisher · View at Google Scholar
  12. J.-C. Rochet, “Rebalancing the three pillars of Basel II,” Economic Policy Review, vol. 10, no. 2, pp. 7–21, 2004.
  13. D. Hancock, A. J. Laing, and J. A. Wilcox, “Bank capital shocks: dynamic effects on securities, loans, and capital,” Journal of Banking & Finance, vol. 19, no. 3-4, pp. 661–677, 1995. View at Publisher · View at Google Scholar
  14. S. Altug and P. Labadie, Dynamic Choice and Asset Markets, Academic Press, San Diego, Calif, USA, 1994.
  15. R. Bliss and G. Kaufman, “Bank procyclicality, credit crunches, and asymmetric monetary policy effects: a unifying model,” Working Paper 2002-18, Federal Reserve Bank of Chicago, Chicago, Ill, USA, 2002.
  16. E. Catarineu-Rabell, P. Jackson, and D. P. Tsomocos, “Procyclicality and the new Basel Accord-banks' choice of loan rating system,” Working Paper 181, Bank of England, London, UK, 2003.
  17. R. Chami and T. F. Cosimano, “Monetary policy with a touch of Basel,” Working Paper 01/151, International Monetary Fund, Washington, DC, USA, 2001. View at Publisher · View at Google Scholar
  18. D. Tsomocos, “Equilibrium analysis, banking, contagion and financial fragility,” Working Paper 175, Bank of England, London, UK, 2003. View at Publisher · View at Google Scholar
  19. S. van den Heuwel, “The bank capital channel of monetary policy,” 2001, Mimeo, University of Pennsylvania.
  20. S. van den Heuwel, “Does bank capital matter for monetary transmission?,” Economic Policy Review, vol. 8, no. 1, pp. 259–265, 2002.
  21. D. Hackbarth, J. Miao, and E. Morellec, “Capital structure, credit risk, and macroeconomic conditions,” Journal of Financial Economics, vol. 82, no. 3, pp. 519–550, 2006. View at Publisher · View at Google Scholar
  22. R. A. Korajczyk and A. Levy, “Capital structure choice: macroeconomic conditions and financial constraints,” Journal of Financial Economics, vol. 68, no. 1, pp. 75–109, 2003. View at Publisher · View at Google Scholar
  23. J. A. Bikker and P. A. J. Metzemakers, “Bank provisioning behaviour and procyclicality,” Journal of International Financial Markets, Institutions and Money, vol. 15, no. 2, pp. 141–157, 2005. View at Publisher · View at Google Scholar
  24. C. Borio, C. Furfine, and P. Lowe, “Procyclicality of the financial system and financial stability: issues and policy options,” Working Paper 1, Bank for International Settlements, Basel, Switzerland, 2001, http://www.bis.org/publ/bispap01a.pdf.
  25. M. Cavallo and G. Majnoni, “Do banks provision for bad loans in good times? empirical evidence and policy implications,” in Ratings, Rating Agencies and the Global Financial System, R. Levich, G. Majnoni, and C. Reinhart, Eds., Kluwer Academics Publishers, Boston, Mass, USA, 2002.
  26. J. Mukuddem-Petersen and M. A. Petersen, “Bank management via stochastic optimal control,” Automatica, vol. 42, no. 8, pp. 1395–1406, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  27. J. Mukuddem-Petersen, M. A. Petersen, I. M. Schoeman, and B. A. Tau, “A profit maximization problem for depository financial institutions,” in Proceedings of the International Conference on Modelling and Optimization of Structures, Processes and Systems (ICMOSPS '07), Durban, South Africa, January 2007.
  28. J. Mukuddem-Petersen, M. A. Petersen, I. M. Schoeman, and B. A. Tau, “An application of stochastic optimization theory to institutional finance,” Applied Mathematical Sciences, vol. 1, no. 28, pp. 1359–1385, 2007.
  29. L. Laeven and G. Majnoni, “Loan loss provisioning and economic slowdowns: too much, too late?,” Journal of Financial Intermediation, vol. 12, no. 2, pp. 178–197, 2003. View at Publisher · View at Google Scholar
  30. T. Björk, Arbitrage Theory in Continuous Time, Oxford University Press, New York, NY, USA, 1998.
  31. The Federal Deposit Insurance Corporation (FDIC), March 2007, http://www2.fdic.gov/qbp/.
  32. R. C. Merton, Continuous-Time Finance, Blackwell Publishers, Cambridge, Mass, USA, 1992.
  33. J. C. Cox and C.-F. Huang, “A variational problem arising in financial economics,” Journal of Mathematical Economics, vol. 20, no. 5, pp. 465–487, 1991. View at Publisher · View at Google Scholar · View at MathSciNet
  34. I. Karatzas, J. P. Lehoczky, and S. E. Shreve, “Optimal portfolio and consumption decisions for a “small investor” on a finite horizon,” SIAM Journal on Control and Optimization, vol. 25, no. 6, pp. 1557–1586, 1987. View at Publisher · View at Google Scholar · View at MathSciNet
  35. C. H. Fouche, J. Mukuddem-Petersen, and M. A. Petersen, “Continuous-time stochastic modelling of capital adequacy ratios for banks,” Applied Stochastic Models in Business and Industry, vol. 22, no. 1, pp. 41–71, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  36. P. Jackson and W. Perraudin, “Regulatory implications of credit risk modelling,” Journal of Banking & Finance, vol. 24, no. 1-2, pp. 1–14, 2000. View at Publisher · View at Google Scholar