Table of Contents Author Guidelines Submit a Manuscript
Discrete Dynamics in Nature and Society
Volume 2016, Article ID 6546318, 7 pages
http://dx.doi.org/10.1155/2016/6546318
Research Article

Operational Risk Aggregation Based on Business Line Dependence: A Mutual Information Approach

1School of Economics and Business Administration, Beijing Normal University, Beijing 100875, China
2Institute of Policy and Management, Chinese Academy of Sciences, Beijing 100190, China

Received 14 January 2016; Accepted 31 March 2016

Academic Editor: Francisco R. Villatoro

Copyright © 2016 Wenzhou Wang 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. J. Li, X. Zhu, J. Chen et al., “Operational risk aggregation across business lines based on frequency dependence and loss dependence,” Mathematical Problems in Engineering, vol. 2014, Article ID 404208, 8 pages, 2014. View at Publisher · View at Google Scholar · View at Scopus
  2. A. Frachot, T. Roncalli, and E. Salomon, “The correlation problem in operational risk,” Working Paper, Groupe de Recherche Operationnelle, Credit Lyonnais, Paris, France, 2004. View at Google Scholar
  3. J. Feng, J. Li, L. Gao, and Z. Hua, “Combination model for operational risk estimation in a Chinese banking industry case,” The Journal of Operational Risk, vol. 7, no. 2, pp. 17–39, 2012. View at Google Scholar
  4. K. Böcker and C. Klüppelberg, “Modeling and measuring multivariate operational risk with Lévy copulas,” Operational Risk, vol. 3, no. 2, pp. 3–27, 2008. View at Google Scholar
  5. Basel Committee on Banking Supervision, International Convergence of Capital Measurement and Capital Standards: A Revised Framework, Bank for International Settlements, Basel, Switzerland, 2004.
  6. J. Li, J. Feng, X. Sun, and M. Li, “Risk integration mechanisms and approaches in banking industry,” International Journal of Information Technology & Decision Making, vol. 11, no. 6, pp. 1183–1213, 2012. View at Publisher · View at Google Scholar · View at Scopus
  7. X. Zhu, Y. Xie, J. Li, and D. Wu, “Change point detection for subprime crisis in American banking: from the perspective of risk dependence,” International Review of Economics and Finance, vol. 38, pp. 18–28, 2015. View at Publisher · View at Google Scholar · View at Scopus
  8. A. Carla, B. Rossella, M. Giovanni, and M. Marco, “Advanced operational risk modeling in banks and insurance companies,” Investment Management and Financial Innovations, vol. 6, no. 3, pp. 73–83, 2009. View at Google Scholar
  9. D. C. Annalisa and R. Claudio, “A copula-extreme value theory approach for modeling operational risk,” in Operational Risk Modelling and Analysis: Theory and Practice, M. Cruz, Ed., Risk Books, 2004. View at Google Scholar
  10. J. Li, X. Zhu, C.-F. Lee, D. Wu, J. Feng, and Y. Shi, “On the aggregation of credit, market and operational risks,” Review of Quantitative Finance and Accounting, vol. 44, no. 1, pp. 161–189, 2015. View at Publisher · View at Google Scholar
  11. A. Dionisio, R. Menezes, and D. A. Mendes, “Mutual information: a measure of dependency for nonlinear time series,” Physica A, vol. 344, no. 1-2, pp. 326–329, 2004. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  12. K. Alexander, S. Harald, and G. Peter, “Estimating mutual information,” Physical Review E, vol. 69, no. 6, pp. 1–16, 2004. View at Google Scholar
  13. J. Li, X. Zhu, Y. Xie et al., “The mutual-information-based variance-covariance approach: an application to operational risk aggregation in Chinese banking,” The Journal of Operational Risk, vol. 9, no. 3, pp. 3–19, 2014. View at Google Scholar
  14. E. Maasoumi and J. Racine, “Entropy and predictability of stock market returns,” Journal of Econometrics, vol. 107, no. 1-2, pp. 291–312, 2002. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  15. G. A. Darbellay and D. Wuertz, “The entropy as a tool for analysing statistical dependences in financial time series,” Physica A: Statistical Mechanics and Its Applications, vol. 287, no. 3-4, pp. 429–439, 2000. View at Publisher · View at Google Scholar · View at Scopus
  16. D. R. Brillinger, “Some data analyses using mutual information,” Brazilian Journal of Probability and Statistics, vol. 18, no. 2, pp. 163–182, 2004. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  17. M. Fernandes and B. Néri, “Nonparametric entropy-based tests of independence between stochastic processes,” Econometric Reviews, vol. 29, no. 3, pp. 276–306, 2010. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  18. C. Granger and J. L. Lin, “Using the mutual information coefficient to identify lags in nonlinear models,” Journal of Time Series Analysis, vol. 15, no. 4, pp. 371–384, 1994. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  19. P. Viola and W. M. Wells III, “Alignment by maximization of mutual information,” International Journal of Computer Vision, vol. 24, no. 2, pp. 137–154, 1997. View at Publisher · View at Google Scholar · View at Scopus
  20. H. Joe, “Relative entropy measures of multivariate dependence,” Journal of the American Statistical Association, vol. 84, no. 405, pp. 157–164, 1989. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  21. H.-P. Bernhard and G. A. Darbellay, “Performance analysis of the mutual information function for nonlinear and linear signal processing,” in Proceedings of the 3rd IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP '99), pp. 1297–1300, Phoenix, Ariz, USA, March 1999. View at Scopus
  22. Basel Committee on Banking Supervision, Operational Risk-Supervisory Guidelines for the Advanced Measurement Approaches, Bank for International Settlements, Basel, Switzerland, 2011.
  23. R. Moddemeijer, “A statistic to estimate the variance of the histogram-based mutual information estimator based on dependent pairs of observations,” Signal Processing, vol. 75, no. 1, pp. 51–63, 1999. View at Publisher · View at Google Scholar · View at Scopus
  24. A. J. Butte and I. S. Kohane, “Mutual information relevance networks: functional genomic clustering using pairwise entropy measurements,” Pacific Symposium on Biocomputing, vol. 5, pp. 418–429, 2000. View at Google Scholar · View at Scopus
  25. A. M. Fraser and H. L. Swinney, “Independent coordinates for strange attractors from mutual information,” Physical Review A, vol. 33, no. 2, pp. 1134–1140, 1986. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  26. C. J. Cellucci, A. M. Albano, and P. E. Rapp, “Statistical validation of mutual information calculations: comparison of alternative numerical algorithms,” Physical Review E-Statistical, Nonlinear, and Soft Matter Physics, vol. 71, no. 6, part 2, Article ID 066208, 2005. View at Publisher · View at Google Scholar · View at Scopus
  27. C. W. Granger, E. Maasoumi, and J. Racine, “A dependence metric for possibly nonlinear processes,” Journal of Time Series Analysis, vol. 25, no. 5, pp. 649–669, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  28. G. A. Darbellay, “An estimator of the mutual information based on a criterion for independence,” Computational Statistics & Data Analysis, vol. 32, no. 1, pp. 1–17, 1999. View at Publisher · View at Google Scholar · View at MathSciNet
  29. G. Darbellay and I. Vadja, “Estimation of the information by an adaptative partitioning of the observation space,” IEEE Transactions on Information Theory, vol. 45, no. 4, pp. 1315–1321, 1999. View at Publisher · View at Google Scholar
  30. A. Dionísio, R. Menezes, and D. A. Mendes, “Entropy-based independence test,” Nonlinear Dynamics, vol. 44, no. 1, pp. 351–357, 2006. View at Publisher · View at Google Scholar · View at Scopus
  31. B. Efron and R. J. Tibshiran, An Introduction to the Bootstrap, Chapman & Hall, New York, NY, USA, 1994.
  32. X. Zhu, J. Li, J. Chen et al., “A nonparametric operational risk modeling approach based on Cornish-Fisher expansion,” Discrete Dynamics in Nature and Society, vol. 2014, Article ID 839731, 8 pages, 2014. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  33. J. Li, J. Feng, and J. Chen, “A piecewise-defined severity distribution-based loss distribution approach to estimate operational risk: evidence from chinese national commercial banks,” International Journal of Information Technology & Decision Making, vol. 8, no. 4, pp. 727–747, 2009. View at Publisher · View at Google Scholar · View at Scopus
  34. L. Gao, J. Li, J. Chen, and W. Xu, “Assessment the operational risk for Chinese commercial banks,” in Computational Science—ICCS 2006, V. N. Alexandrov, G. D. van Albada, P. M. A. Sloot, and J. Dongarra, Eds., vol. 3994 of Lecture Notes in Computer Science, pp. 501–508, 2006. View at Publisher · View at Google Scholar
  35. J. Feng, J. Chen, and J. Li, “Operational risk measurement via the loss distribution approach,” in Proceedings of the IEEE International Conference on Grey Systems and Intelligent Services (GSIS '09), pp. 1744–1748, Nanjing, China, November 2009. View at Publisher · View at Google Scholar · View at Scopus
  36. G. Rosella, R. Svetlozar, C. Anna, and B. Marida, “Aggregation issues in operational risk,” The Journal of Operational Risk, vol. 3, no. 3, pp. 1–23, 2008. View at Publisher · View at Google Scholar
  37. A. Chapelle, Y. Crama, G. Hübner, and J.-P. Peters, “Practical methods for measuring and managing operational risk in the financial sector: a clinical study,” Journal of Banking and Finance, vol. 32, no. 6, pp. 1049–1061, 2008. View at Publisher · View at Google Scholar · View at Scopus