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