Abstract: We present a theoretical framework for stressing multivariate stochastic models. We consider a stress to be a change of measure, placing a higher weight on multivariate scenarios of interest. In particular, a stressing mechanism is a mapping from random vectors to Radon-Nikodym densities. We postulate desirable properties for stressing mechanisms addressing alternative objectives. Consistently with our focus on dependence, we require throughout invariance to monotonic transformations of risk factors. We study in detail the properties of two families of stressing mechanisms, based respectively on mixtures of univariate stresses and on transformations of statistics we call Spearman and Kendall's cores. Furthermore, we characterize the aggregation properties of those stressing mechanisms, which motivate their use in deriving new capital allocation methods, with properties different to those typically found in the literature. The proposed methods are applied to stress testing and capital allocation, using the simulation model of a UK-based non-life insurer.
About: Andreas Tsanakas is Professor in Risk Management at Bayes Business School (formerly Cass), City, University of London, and Editor-in-Chief of the Annals of Actuarial Science. His research interests range from quantitative risk management to sensitivity analysis, model uncertainty, and the role of models as decision tools in financial organisations. He has won industry research awards for his work on capital allocation, model risk and sensitivity analysis. Andreas is co-organiser of the Insurance Data Science Conference and the One World Actuarial Research Seminar.
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Meeting ID: 792 221 9559