Article
MSC:
62E17,
62H20,
62P99,
65C20,
91B30,
91G50,
91G60 | MR 3455170 | Zbl 06562149 | DOI: 10.1007/s10492-016-0124-z
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Keywords:
mixed operation; grouped model; aggregated risk measurement; Value of Risk; numerical simulation
mixed operation; grouped model; aggregated risk measurement; Value of Risk; numerical simulation
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.
References:
[1] Allen, L., Rai, A.: Operational efficiency in banking: An international comparison. Journal of Banking & Finance 20 (1996), 655-672. DOI 10.1016/0378-4266(95)00026-7
[2] Arbenz, P., Hummel, C., Mainik, G.: Copula based hierarchical risk aggregation through sample reordering. Insur. Math. Econ. 51 (2012), 122-133. DOI 10.1016/j.insmatheco.2012.03.009 | MR 2928749 | Zbl 1284.91198
[3] Berger, A. N., Demsetz, R. S., Strahan, P. E.: The consolidation of the financial services industry: Causes, consequences, and implications for the future. Journal of Banking & Finance 23 (1999), 135-194. DOI 10.1016/S0378-4266(98)00125-3
[4] Bernard, C., Jiang, X., Wang, R.: Risk aggregation with dependence uncertainty. Insur. Math. Econ. 54 (2014), 93-108. DOI 10.1016/j.insmatheco.2013.11.005 | MR 3145855 | Zbl 1291.91090
[5] Chong, B., Liu, M., Altunbaş, Y.: 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] Denuit, M., Genest, C., Marceau, É.: Stochastic bounds on sums of dependent risks. Insur. Math. Econ. 25 (1999), 85-104. DOI 10.1016/S0167-6687(99)00027-X | MR 1718543 | Zbl 1028.91553
[7] Embrechts, P., Höing, A., Juri, A.: Using copulae to bound the value-at-risk for functions of dependent risks. Finance Stoch. 7 (2003), 145-167. DOI 10.1007/s007800200085 | MR 1968943 | Zbl 1039.91023
[8] Embrechts, P., Puccetti, G., Rüschendorf, L.: Model uncertainty and VaR aggregation. Journal of Banking & Finance 37 (2013), 2750-2764. DOI 10.1016/j.jbankfin.2013.03.014
[9] Fields, L. P., Fraser, D. R.: 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] Frei, F. X., Harker, P. T., Hunter, L. W.: Inside the Black Box: What Makes a Bank Efficient? Financial Institutions. Efficiency, Innovation, Regulation (eds. P. Harker, S. Zenios) Cambridge University Press (2000).
[11] Hashorva, E.: Exact tail asymptotics of aggregated parametrised risk. J. Math. Anal. Appl. 400 (2013), 187-199. DOI 10.1016/j.jmaa.2012.11.047 | MR 3003975 | Zbl 1258.91104
[12] Heilpern, S.: Aggregate dependent risks-risk measure calculation. Mathematical Economics 7 (2011), 107-122.
[13] Joe, H., Li, H., Nikoloulopoulos, A. K.: Tail dependence functions and vine copulas. J. Multivariate Anal. 101 (2010), 252-270. DOI 10.1016/j.jmva.2009.08.002 | MR 2557632 | Zbl 1177.62072
[14] Junker, M., May, A.: Measurement of aggregate risk with copulas. Econom. J. 8 (2005), 428-454. DOI 10.1111/j.1368-423X.2005.00173.x | MR 2188967 | Zbl 1125.91351
[15] Mao, S., Wang, J., Pu, X.: Advanced Mathematical Statistics. Higher Education Press, Beijing (2006).
[16] Markowitz, H.: Portfolio selection. The Journal of Finance 7 (1952), 77-91.
[17] McNeil, A. J., Frey, R., Embrechts, P.: Quantitative Risk Management. Concepts, Techniques, and Tools. Princeton Series in Finance Princeton University Press, Princeton (2005). MR 2175089 | Zbl 1089.91037
[18] Rime, B., Stiroh, K. J.: 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] Rüschendorf, L.: Random variables with maximum sums. Adv. Appl. Probab. 14 (1982), 623-632. DOI 10.2307/1426677 | MR 0665297 | Zbl 0487.60026
[20] Skoglund, J., Erdman, D., Chen, W.: A mixed approach to risk aggregation using hierarchical copulas. Journal of Risk Management in Financial Institutions 6 (2013), 188-205.
[21] Wang, R., Peng, L., Yang, J.: Bounds for the sum of dependent risks and worst value-at-risk with monotone marginal densities. Finance Stoch. 17 (2013), 395-417. DOI 10.1007/s00780-012-0200-5 | MR 3038596 | Zbl 1266.91038
[22] Wang, B., Wang, R.: The complete mixability and convex minimization problems with monotone marginal densities. J. Multivariate Anal. 102 (2011), 1344-1360. DOI 10.1016/j.jmva.2011.05.002 | MR 2819953 | Zbl 1229.60019
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