### Mathematics Colloquium

** Alexander Schied
**

University of Waterloo

**Title:** Robustness in risk measurement: the impact of incentives

**Date:** Friday, February 19, 2021

**Place and Time:** Zoom, 3:05-3:55 pm

**Abstract.**
Statistical robustness is a desirable property for a regulatory risk measure. Previous research has stressed that Value at Risk is more robust than Expected Shortfall if both are applied to the same financial position. In reality, however, the regulatory choice of a particular risk measure imposes certain incentives, which impact the underlying position even before a particular risk measure is applied. Thus, one cannot decouple the technical properties of a risk measure from the incentives it creates. In this talk, we describe a first attempt of taking such incentives into account when assessing a risk measure’s robustness properties. To this end, we develop a general methodology which we call “robustness against optimization”. The new notion is studied for various classes of risk measures and expected utility and loss. In doing so, we arrive at conclusions, which are different from those of the previous literature and perhaps somewhat surprising. The talk is based on joint work with Paul Embrechts and Ruodu Wang.