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Volume 5/Issue 2, Summer 2010 Research Papers Calculation of aggregate loss distributions Pavel V. Shevchenko
CSIRO Mathematics, Informatics and Statistics, Locked Bag 17, North Ryde, NSW 1670, Sydney, Australia; email: Pavel.Shevchenko@csiro.au 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. In addition, several closed-form approximations based on moment matching and asymptotic results for heavy-tailed distributions are reviewed.
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