Calculation of aggregate loss distributions

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.

Rapidly bounding the exceedance probabilities of high aggregate losses

“…There are several approaches to computing Pr(S t ≥ s) to arbitrary accuracy, although in practice this accuracy is limited by computing power (see Shevchenko, 2010, for a review). We mention two here.…”

Impact of interference on the coverage and connectivity of Ad hoc networks in a fading environment

“…The skewness parameter is defined by the ratio 3 ( 2 ) 3/2 , where the k-th central moment of the random variable Z about its mean is given by k = E (Z − E(Z)) k . The first four central moments of the compound Poisson sum about the mean, where K is a Poisson random variable with parameter M , are given by [21] The three parameters of the shifted-gamma distribution can be obtained by matching the mean, variance, and skewness of Z to those of to give [20]…”

“…(10), (20), and (21). The node density * M , called critical node density, that yields a given probability of network connectivity, say P con = p*, may be obtained from Eq.…”

Construcción de la distribución de pérdidas y el problema de agregación de riesgo operativo bajo modelos LDA: una revisión

“…Otro artículo donde se realizan comparaciones de los métodos mencionados es el de Shevchenko [27], quien concluye que cada método tiene sus fortalezas y debilidades. Por ejemplo, la simulación Monte Carlo es lenta pero es fácil de implementar y permite modelar dependencia.…”