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 …

Equivalent characterizations of multi-portfolio time consistency are deduced for closed
convex and coherent set-valued risk measures on L^p(\varOmega,F,P;R^d) with image …

We investigate to which extent the relevant features of (static) Systemic Risk Measures can
be extended to a conditional setting. After providing a general dual representation result, we …

A method for calculating multi-portfolio time consistent multivariate risk measures in discrete
time is presented. Market models for d assets with transaction costs or illiquidity and …

Risk measures for multivariate financial positions are studied in a utility-based framework.
Under a certain incomplete preference relation, shortfall and divergence risk measures are …

In this paper, we propose a Newton method for unconstrained set optimization problems to
find its weakly minimal solutions with respect to lower set-less ordering. The objective …

In this paper we present results on dynamic multivariate scalar risk measures, which arise in
markets with transaction costs and systemic risk. Dual representations of such risk measures …

In this paper, we introduce two kinds of time consistent properties for set-valued dynamic risk
measures for discrete-time processes that are adapted to a given filtration, named time …

In this paper, we consider set optimization problems where the solution concept is given by
the set approach. Specifically, we deal with the lower less and the upper less set relations …

In this paper we study the path-regularity and martingale properties of the set-valued
stochastic integrals defined in our previous work Ararat et al.(2023). Such integrals have …