Set-valued dynamic risk measures are defined on <inline-formula id="ILM0001"> <inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="rquf_a_781668_o_ilm0001.gif"/> </inline-formula> with <inline-formula id="ILM0002"> <inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="rquf_a_781668_o_ilm0002.gif"/> </inline-formula> and with an image space in the power set of <inline-formula id="ILM0003"> <inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="rquf_a_781668_o_ilm0003.gif"/> </inline-formula>. Primal and dual representations of dynamic risk measures are deduced. Definitions of different time consistency properties in the set-valued framework are given. It is shown that the...

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...

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....

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...

<Para ID="Par1">Equivalent characterizations of multi-portfolio time consistency are deduced for closed convex and coherent set-valued risk measures on <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$L^{p}({\varOmega,\mathcal{F},\mathbb{P}; \mathbb{R}^{d}})$</EquationSource> </InlineEquation> with image space in the power set of <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$L^{p}({\varOmega,\mathcal{F}_{t},\mathbb{P};...</equationsource></inlineequation></equationsource></inlineequation></para>

New versions and extensions of Benson’s outer approximation algorithm for solving linear vector optimization problems are presented. Primal and dual variants are provided in which only one scalar linear program has to be solved in each iteration rather than two or three as in previous...

We study the explicit calculation of the set of superhedging portfolios of contingent claims in a discrete-time market model for d assets with proportional transaction costs. The set of superhedging portfolios can be obtained by a recursive construction involving set operations, going backward...

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...