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Calculation of aggregate loss distributions

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  • Pavel V. Shevchenko

Abstract

Estimation of the operational risk capital under the Loss Distribution Approach requires evaluation of aggregate (compound) loss distributions which is one of the classic problems in risk theory. Closed-form solutions are not available for the distributions typically used in operational risk. However with modern computer processing power, these distributions can be calculated virtually exactly using numerical methods. This paper reviews numerical algorithms that can be successfully used to calculate the aggregate loss distributions. In particular Monte Carlo, Panjer recursion and Fourier transformation methods are presented and compared. Also, several closed-form approximations based on moment matching and asymptotic result for heavy-tailed distributions are reviewed.

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  • Pavel V. Shevchenko, 2010. "Calculation of aggregate loss distributions," Papers 1008.1108, arXiv.org.
  • Handle: RePEc:arx:papers:1008.1108
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    File URL: http://arxiv.org/pdf/1008.1108
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    References listed on IDEAS

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    4. Marco Moscadelli, 2004. "The modelling of operational risk: experience with the analysis of the data collected by the Basel Committee," Temi di discussione (Economic working papers) 517, Bank of Italy, Economic Research and International Relations Area.
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    6. Vernic, Raluca, 1999. "Recursive Evaluation of Some Bivariate Compound Distributions," ASTIN Bulletin: The Journal of the International Actuarial Association, Cambridge University Press, vol. 29(02), pages 315-325, November.
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    8. Bladt, Mogens, 2005. "A Review on Phase-type Distributions and their Use in Risk Theory," ASTIN Bulletin: The Journal of the International Actuarial Association, Cambridge University Press, vol. 35(01), pages 145-161, May.
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    10. H. Panjer, Harry & Shaun Wang, 2, 1993. "On the Stability of Recursive Formulas," ASTIN Bulletin: The Journal of the International Actuarial Association, Cambridge University Press, vol. 23(02), pages 227-258, November.
    11. Panjer, Harry H. & Willmot, Gordon E., 1986. "Computational aspects of recursive evaluation of compound distributions," Insurance: Mathematics and Economics, Elsevier, vol. 5(1), pages 113-116, January.
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    Cited by:

    1. Mora Valencia Andrés, 2014. "El uso de la distribución g-h en riesgo operativo," Contaduría y Administración, Accounting and Management, vol. 59(1), pages 123-148, enero-mar.
    2. Kensuke Ishitani & Kenichi Sato, 2013. "An Analytical Evaluation Method of the Operational Risk Using Fast Wavelet Expansion Techniques," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 20(3), pages 283-309, September.
    3. Eckert, Christian & Gatzert, Nadine, 2017. "Modeling operational risk incorporating reputation risk: An integrated analysis for financial firms," Insurance: Mathematics and Economics, Elsevier, vol. 72(C), pages 122-137.

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