Dual representations for systemic risk measures

Dual Representations for Convex Risk Measures via Conjugate Duality

The aim of this paper is to give dual representations for different convex risk measures by employing their conjugate functions. To establish the formulas for the conjugates, we use on the one hand some classical results from convex analysis and on the other hand some tools from the conjugate duality theory. Some characterizations of so-called deviation measures recently given in the literature...

Looking for appropriate qualification conditions for subdifferential formulae and dual representations for convex risk measures

A fruitful idea, when providing subdifferential formulae and dual representations for convex risk measures, is to make use of the conjugate duality theory in convex optimization. In this paper we underline the outstanding role played by the qualification conditions in the context of different problem formulations in this area. We show that not only the meanwhile classical generalized interiorit...

Measures of Systemic Risk

Subdifferential representations of risk measures

Measures of risk appear in two categories: Risk capital measures serve to determine the necessary amount of risk capital in order to avoid ruin if the outcomes of an economic activity are uncertain and their negative values may be interpreted as acceptability measures (safety measures). Pure risk measures (risk deviation measures) are natural generalizations of the standard deviation. While pur...

Systemic risk measures: the simpler the better?

The financial system plays a fundamental role in the global economy as the middleman between agents who need to borrow and agents who are willing to lend or invest. As a consequence, it is naturally linked to all economic sectors and, therefore, if the financial system does not work properly, its problems have a strong impact on the real economy. We can see this in the deteriorating fundamental...