A theory of multivariate stress testing

We present a theoretical framework for stressing multivariate stochastic models. consider stress to be change of measure, placing higher weight on scenarios interest. In particular, mechanism is mapping from random vectors RadonNikodym densities. postulate desirable properties mechanisms addressing alternative objectives. Consistently with our focus dependence, we require throughout invariance monotonic transformations risk factors. study in detail the two families mechanisms, based respectively mixtures univariate stresses and statistics call Spearman Kendall’s cores. Furthermore, characterize aggregation those which motivate their use deriving new capital allocation methods, different typically found literature. The proposed methods are applied testing allocation, using simulation model UK-based non-life insurer.