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Calculation of aggregate loss distributions

  • Pavel V. Shevchenko
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    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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    File URL: http://arxiv.org/pdf/1008.1108
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    Paper provided by arXiv.org in its series Papers with number 1008.1108.

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    Date of creation: Aug 2010
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    Publication status: Published in The Journal of Operational Risk 5(2), pp. 3-40, 2010
    Handle: RePEc:arx:papers:1008.1108
    Contact details of provider: Web page: http://arxiv.org/

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    1. Grübel, Rudolf & Hermesmeier, Renate, 1999. "Computation of Compound Distributions I: Aliasing Errors and Exponential Tilting," ASTIN Bulletin: The Journal of the International Actuarial Association, Cambridge University Press, vol. 29(02), pages 197-214, November.
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    6. repec:spr:compst:v:69:y:2009:i:3:p:497-508 is not listed on IDEAS
    7. 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.
    8. 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.
    9. 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.
    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.
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