×

Copula-based grouped risk aggregation under mixed operation. (English) Zbl 1389.91140

Summary: 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.

MSC:

91G70 Statistical methods; risk measures
62H20 Measures of association (correlation, canonical correlation, etc.)
62E17 Approximations to statistical distributions (nonasymptotic)
91G60 Numerical methods (including Monte Carlo methods)

Software:

QRM
PDFBibTeX XMLCite
Full Text: DOI Link

References:

[1] L. Allen, A. Rai: Operational efficiency in banking: An international comparison. Journal of Banking & Finance 20 (1996), 655-672. · doi:10.1016/0378-4266(95)00026-7
[2] P. Arbenz, C. Hummel, G. Mainik: Copula based hierarchical risk aggregation through sample reordering. Insur. Math. Econ. 51 (2012), 122-133. · Zbl 1284.91198 · doi:10.1016/j.insmatheco.2012.03.009
[3] Berger, A. N.; Demsetz, R. S.; Strahan, P. E., No article title, The consolidation of the financial services industry: Causes, consequences, and implications for the future. Journal of Banking & Finance, 23, 135-194 (1999)
[4] C. Bernard, X. Jiang, R. Wang: Risk aggregation with dependence uncertainty. Insur. Math. Econ. 54 (2014), 93-108. · Zbl 1291.91090 · doi:10.1016/j.insmatheco.2013.11.005
[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. · doi:10.1016/0927-538X(96)00010-8
[6] M. Denuit, C. Genest, É. Marceau: Stochastic bounds on sums of dependent risks. Insur. Math. Econ. 25 (1999), 85-104. · Zbl 1028.91553 · doi:10.1016/S0167-6687(99)00027-X
[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. · Zbl 1039.91023 · doi:10.1007/s007800200085
[8] Embrechts, P.; Puccetti, G.; Rüschendorf, L., No article title, Model uncertainty and VaR aggregation. Journal of Banking & Finance, 37, 2750-2764 (2013) · doi:10.1016/j.jbankfin.2013.03.014
[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. · doi:10.1016/S0378-4266(99)00010-2
[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. · Zbl 1039.91023
[11] E. Hashorva: Exact tail asymptotics of aggregated parametrised risk. J. Math. Anal. Appl. 400 (2013), 187-199. · Zbl 1258.91104 · doi:10.1016/j.jmaa.2012.11.047
[12] Heilpern, S., No article title, Aggregate dependent risks-risk measure calculation. Mathematical Economics, 7, 107-122 (2011)
[13] H. Joe, H. Li, A. K. Nikoloulopoulos: Tail dependence functions and vine copulas. J. Multivariate Anal. 101 (2010), 252-270. · Zbl 1177.62072 · doi:10.1016/j.jmva.2009.08.002
[14] M. Junker, A. May: Measurement of aggregate risk with copulas. Econom. J. 8 (2005), 428-454. · Zbl 1125.91351 · doi:10.1111/j.1368-423X.2005.00173.x
[15] S. Mao, J. Wang, X. Pu: Advanced Mathematical Statistics. Higher Education Press, Beijing, 2006.
[16] H. Markowitz: Portfolio selection. The Journal of Finance 7 (1952), 77-91.
[17] A. J. McNeil, R. Frey, P. Embrechts: Quantitative Risk Management. Concepts, Techniques, and Tools. Princeton Series in Finance, Princeton University Press, Princeton, 2005. · Zbl 1089.91037
[18] B. Rime, K. J. Stiroh: The performance of universal banks: Evidence from Switzerland. Journal of Banking & Finance 27 (2003), 2121-2150. · doi:10.1016/S0378-4266(02)00318-7
[19] L. Rüschendorf: Random variables with maximum sums. Adv. Appl. Probab. 14 (1982), 623-632. · Zbl 0487.60026 · doi:10.2307/1426677
[20] Skoglund, J.; Erdman, D.; Chen, W., No article title, A mixed approach to risk aggregation using hierarchical copulas. Journal of Risk Management in Financial Institutions, 6, 188-205 (2013)
[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. · Zbl 1266.91038 · doi:10.1007/s00780-012-0200-5
[22] B. Wang, R. Wang: The complete mixability and convex minimization problems with monotone marginal densities. J. Multivariate Anal. 102 (2011), 1344-1360. · Zbl 1229.60019 · doi:10.1016/j.jmva.2011.05.002
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.