Abstract:
The quantitative regulation of banking and insurance is very much based on specific risk measures. Examples include Value-at-Risk (a quantile based measure) and Expected Shortfall (a conditional excess measure). Besides their statistical estimation, recent applications very much use the axiomatic theory of risk measures to investigate allocation and aggregation properties. In this talk I will present the necessary theory (going back to a question of Kolmogorov) on quantile based risk aggregation when only partial information on the underlying stochastic structure is known. Besides discussing some analytic results for sums of risk positions, I will also present a versatile, so-called Rearrangement Algorithm for the numerical calculation of best and worst bounds in a model uncertainty context. As an example we discuss the calculation of risk capital for operational risk within the Basel 3 framework of banking regulation.