Colloquium: Robust Risk Measures: Static to Dynamic

In this talk I discuss robust risk measures - also called worst-case risk measures – which are the largest value a risk measure can attain within an uncertainty set. An uncertainty set is defined as a set of random variables which are considered as plausible alternatives and are typically characterised by balls around a reference random variable. Examples include robust distortion risk measures and uncertainty sets induced by the Wasserstein distance and moment constraints. 

I further consider the dynamic setting, where the risk of stochastic processes is evaluated using time-consistent dynamic risk measures. In the dynamic setting we introduce dynamic uncertainty sets which quantify at each point in time the uncertainty of the future process. We discuss conditions on the uncertainty sets that lead to well-known properties of dynamic robust risk measures, such as convexity and coherence. Furthermore, we proof necessary and sufficient properties of dynamic uncertainty sets that lead to time-consistency of robust dynamic risk measures.