Recent developments in set optimization are surveyed and extended including various set
relations as well as fundamental constructions of a convex analysis for set-and vector …

The ongoing concern about systemic risk since the outburst of the global financial crisis has
highlighted the need for risk measures at the level of sets of interconnected financial …

Since risky positions in multivariate portfolios can be offset by various choices of capital
requirements that depend on the exchange rules and related transaction costs, it is natural …

We consider the problem of finding (Pareto-) optimal allocations of risk among finitely many
agents. The associated individual risk measures are law-invariant, but with respect to agent …

We present a theoretical framework for stressing multivariate stochastic models. We
consider a stress to be a change of measure, placing a higher weight on multivariate …

We show how risk measures originally defined in a model free framework in terms of
acceptance sets and reference assets imply a meaningful underlying probability structure …

In a capital adequacy framework, risk measures are used to determine the minimal amount
of capital that a financial institution has to raise and invest in a portfolio of prespecified …

The financial crisis showed the importance of measuring, allocating and regulating systemic
risk. Recently, the systemic risk measures that can be decomposed into an aggregation …

This paper addresses the Entropic Value-at-Risk (EV@ R EV@ R), a recently introduced
coherent risk measure. It is demonstrated that the norms defined by EV@ R EV@ R induce …

We establish dual representations for systemic risk measures based on acceptance sets in a
general setting. We deal with systemic risk measures of both “first allocate, then aggregate” …