Aggregating risk capital, with an application to operational risk

Abstract We describe a numerical procedure to obtain bounds on the distribution function of a sum of n dependent risks having fixed marginals. With respect to the existing literature, our method provides improved bounds and can be applied also to large non-homogeneous portfolios of risks. As an application, we compute the VaR-based minimum capital requirement for a portfolio of operational risk losses. Key words risk aggregation – dependency bounds – operational risk – mass transportation duality theorem – global optimizatio