Il giorno martedì 30 maggio alle ore 16.30, presso la Aula Seminari del DISMEQ al IV piano dell'edificio U7, il prof. Ruodu Wang della Università di Waterloo terrà un seminario su

A theory for measures of tail risk

Abstract

The notion of “tail risk” has been a crucial consideration in modern risk management. To achieve a comprehensive understanding of the tail risk, we carry out an axiomatic study for risk measures which quantify the tail risk, that is, the behavior of a risk beyond a certain quantile. Such risk measures are referred to as tail risk measures in this talk. The two popular classes of regulatory risk measures in banking and insurance, the Value-at-Risk (VaR) and the Expected Shortfall (ES), are prominent, yet elementary, examples of tail risk measures. We establish a connection between a tail risk measure and a corresponding law-invariant risk measure, called its generator, and investigate their joint properties. A tail risk measure inherits many properties from its generator, but not subadditivity or convexity; nevertheless, a tail risk measure is coherent if and only if its generator is coherent. We explore further relevant issues on tail risk measures, such as bounds, distortion risk measures, risk aggregation, elicitability, and dual representations. In particular, there is no elicitable tail convex risk measure other than the essential supremum, and under a continuity condition, the only elicitable and positively homogeneous monetary tail risk measures are the VaRs. The study on tail risk measures brings in new tools and insights for prudent risk management as highlighted in the recent Basel documents on financial regulation. This talk focuses on mathematical developments of the theory (joint work with Fangda Liu).

Tutti gli interessati sono invitati a partecipare.

Fabio Bellini