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 …

Two approximation algorithms for solving convex vector optimization problems (CVOPs) are
provided. Both algorithms solve the CVOP and its geometric dual problem simultaneously …

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 …

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 …

In this paper, we propose a novel multivariate shortfall risk measure to evaluate the systemic
risk of a financial system, where the allocation weight is scenario-dependent and optimally …

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 …

This paper contains an overview of results for dynamic multivariate risk measures. We
provide the main results of four different approaches. We will prove under which …

A new operator for handling the joint risk of different sources has been presented and its
various properties are investigated. The problem of risk evaluation of multivariate risk …

Risk measures for random vectors have been considered in multiasset markets with
transaction costs and financial networks in the literature. While the theory of set-valued risk …

Scalar dynamic risk measures for univariate positions in continuous time are commonly
represented via backward stochastic differential equations. In the multivariate setting …