Approximation of Aggregate and Extremal Losses within the Very Heavy Tails Framework

The loss distribution approach (LDA) is one of the three advanced measurement approaches (AMA) to the Pillar I modelling proposed by Basel II in 2001. In this paper, one possible approximation of the aggregate and maximum loss distribution in the extremely Low Frequency/High Severity case, i.e. the case of infinite mean of the loss sizes and loss inter-arrival times. In this study independent but not identically distributed losses are considered. The minimum loss amount is considered increasing over time. Monte Carlo simulation algorithm is given and several quantiles are estimated. The same approximation is in place for modelling the maximum and aggregate worldwide economy losses caused by very rare and very extreme events such as 9/11, the Russian rouble crisis, and the U.S. subprime mortgage crisis.