This paper is concerned with the utility-based risk of a financial position in a multi-asset market with frictions. Risk is quantified by set-valued risk measures, and market frictions are modeled by conical/convex random solvency regions representing proportional transaction costs or...

Systemic risk refers to the risk that the financial system is susceptible to failures due to the characteristics of the system itself. The tremendous cost of this type of risk requires the design and implementation of tools for the efficient macroprudential regulation of financial institutions....

Equivalent characterizations of multiportfolio time consistency are deduced for closed convex and coherent set-valued risk measures on $L^p(\Omega,\mathcal F, P; R^d)$ with image space in the power set of $L^p(\Omega,\mathcal F_t,P;R^d)$. In the convex case, multiportfolio time consistency is...

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 assumptions results within these approaches coincide, and how properties like primal and dual representation and time consistency...

We develop a duality theory for weakly minimal points of multiple objective linear programs which has several advantages in contrast to other theories. For instance, the dual variables are vectors rather than matrices and the dual feasible set is a polyhedron. We use a set-valued dual objective...

This paper considers credit default swaps (CDSs) used for the transfer of credit risk within the banking sector. The banks' motive to conclude these CDS contracts is to improve the diversification of their credit risk. It is shown that these CDSs "reduce" the stability of the banking sector in a...

We develop a duality theory for weakly minimal points of multiple objective linear programs which has several advantages in contrast to other theories. For instance, the dual variables are vectors rather than matrices and the dual feasible set is a polyhedron. We use a set-valued dual objective...

This paper considers credit default swaps (CDS) used for the transfer of credit risk within the banking sector. The banks' motive to conclude these CDS contracts is to improve the diversification of their credit risks. It is shown that these CDS reduce the stability of the banking sector in a...

In incomplete financial markets not every contingent claim can be replicated by a self-financing strategy. The risk of the resulting shortfall can be measured by convex risk measures, recently introduced by Follmer and Schied (2002). The dynamic optimization problem of finding a self-financing...