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Copula-based grouped risk aggregation under mixed operation

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Abstract

This paper deals with the problem of risk measurement under mixed operation. For this purpose, we divide the basic risks into several groups based on the actual situation. First, we calculate the bounds for the subsum of every group of basic risks, then we obtain the bounds for the total sum of all the basic risks. For the dependency relationships between the basic risks in every group and all of the subsums, we give different copulas to describe them. The bounds for the aggregated risk under mixed operation and the algorithm for numerical simulation are given in this paper. In addition, the convergence of the algorithm is proved and some numerical simulations are presented.

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References

  1. L. Allen, A. Rai: Operational efficiency in banking: An international comparison. Journal of Banking & Finance 20 (1996), 655–672.

    Article  Google Scholar 

  2. P. Arbenz, C. Hummel, G. Mainik: Copula based hierarchical risk aggregation through sample reordering. Insur. Math. Econ. 51 (2012), 122–133.

    Article  MathSciNet  MATH  Google Scholar 

  3. A. N. Berger, R. S. Demsetz, P. E. Strahan: The consolidation of the financial services industry: Causes, consequences, and implications for the future. Journal of Banking & Finance 23 (1999), 135–194.

    Google Scholar 

  4. C. Bernard, X. Jiang, R. Wang: Risk aggregation with dependence uncertainty. Insur. Math. Econ. 54 (2014), 93–108.

    Article  MathSciNet  MATH  Google Scholar 

  5. B. Chong, M. Liu, Y. Altunbaş: The impact of universal banking on the risks and returns of Japanese financial institutions. Pacific-Basin Finance Journal 4 (1996), 181–195.

    Article  Google Scholar 

  6. M. Denuit, C. Genest, É. Marceau: Stochastic bounds on sums of dependent risks. Insur. Math. Econ. 25 (1999), 85–104.

    Article  MathSciNet  MATH  Google Scholar 

  7. P. Embrechts, A. Höing, A. Juri: Using copulae to bound the value-at-risk for functions of dependent risks. Finance Stoch. 7 (2003), 145–167.

    Article  MathSciNet  MATH  Google Scholar 

  8. P. Embrechts, G. Puccetti, L. Rüschendorf: Model uncertainty and VaR aggregation. Journal of Banking & Finance 37 (2013), 2750–2764.

    Article  Google Scholar 

  9. L. P. Fields, D. R. Fraser: On the compensation implications of commercial bank entry into investment banking. Journal of Banking & Finance 23 (1999), 1261–1276.

    Article  Google Scholar 

  10. F. X. Frei, P. T. Harker, L. W. Hunter: Inside the Black Box: What Makes a Bank Efficient? Financial Institutions. Efficiency, Innovation, Regulation (eds. P. Harker, S. Zenios), Cambridge University Press, 2000.

  11. E. Hashorva: Exact tail asymptotics of aggregated parametrised risk. J. Math. Anal. Appl. 400 (2013), 187–199.

    Article  MathSciNet  MATH  Google Scholar 

  12. S. Heilpern: Aggregate dependent risks-risk measure calculation. Mathematical Economics 7 (2011), 107–122.

    Google Scholar 

  13. H. Joe, H. Li, A. K. Nikoloulopoulos: Tail dependence functions and vine copulas. J. Multivariate Anal. 101 (2010), 252–270.

    Article  MathSciNet  MATH  Google Scholar 

  14. M. Junker, A. May: Measurement of aggregate risk with copulas. Econom. J. 8 (2005), 428–454.

    Article  MathSciNet  MATH  Google Scholar 

  15. S. Mao, J. Wang, X. Pu: Advanced Mathematical Statistics. Higher Education Press, Beijing, 2006.

    Google Scholar 

  16. H. Markowitz: Portfolio selection. The Journal of Finance 7 (1952), 77–91.

    Google Scholar 

  17. A. J. McNeil, R. Frey, P. Embrechts: Quantitative Risk Management. Concepts, Techniques, and Tools. Princeton Series in Finance, Princeton University Press, Princeton, 2005.

    MATH  Google Scholar 

  18. B. Rime, K. J. Stiroh: The performance of universal banks: Evidence from Switzerland. Journal of Banking & Finance 27 (2003), 2121–2150.

    Article  Google Scholar 

  19. L. Rüschendorf: Random variables with maximum sums. Adv. Appl. Probab. 14 (1982), 623–632.

    Article  MATH  Google Scholar 

  20. J. Skoglund, D. Erdman, W. Chen: A mixed approach to risk aggregation using hierarchical copulas. Journal of Risk Management in Financial Institutions 6 (2013), 188–205.

    Google Scholar 

  21. R. Wang, L. Peng, J. Yang: Bounds for the sum of dependent risks and worst value-atrisk with monotone marginal densities. Finance Stoch. 17 (2013), 395–417.

    Article  MathSciNet  MATH  Google Scholar 

  22. B. Wang, R. Wang: The complete mixability and convex minimization problems with monotone marginal densities. J. Multivariate Anal. 102 (2011), 1344–1360.

    Article  MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. Zhejiang Gongshang University, 18 Xuezheng St, Jianggan, Hangzhou, Zhejiang, China

    Quan Zhou, Zhenlong Chen & Ruixing Ming

Authors
  1. Quan Zhou
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  2. Zhenlong Chen
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  3. Ruixing Ming
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Corresponding author

Correspondence to Zhenlong Chen.

Additional information

Supported by the National Natural Science Foundation of China (11371321).

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Zhou, Q., Chen, Z. & Ming, R. Copula-based grouped risk aggregation under mixed operation. Appl Math 61, 103–120 (2016). https://doi.org/10.1007/s10492-016-0124-z

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  • DOI: https://doi.org/10.1007/s10492-016-0124-z

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