"Risk measures in financial mathematics"
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
Place: Mathematics Seminar Room, SA-141
Tea and cookies will be served before the seminar.