**"****Risk measures in financial mathematics****"**

By

**ÇAĞIN ARARAT**

**(BİLKENT UNIVERSITY)**

**Abstract:**** ** A
risk measure is a monotone convex real-valued functional on a certain space of
random variables. In financial mathematics, the position in a risky asset (e.g.
stock, currency, gold) whose terminal value is subject to uncertainty is
typically modeled as a random variable and a risk
measure quantifies the deterministic capital requirement for such a position.
The theory of risk measures has been developed in the last fifteen years and is
still an active area of research with applications in stochastic optimization,
portfolio optimization and systemic risk. In this talk, we will discuss some
basic properties and examples of risk measures as well as their dual
representations in terms of probability measures, which
can be obtained by an application of the Fenchel-Moreau
biconjugation theorem in convex analysis. In the last
part of the talk, we will briefly discuss the concept of multivariate risk,
more precisely, set-valued risk measures for random vectors, and their
applications to systemic risk.

**Date: ****Monday, February 22, 2016**

**Time: ****15.40**

**Place: ****Mathematics Seminar Room,
SA-141**

Tea and cookies will be served before the
seminar.