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...

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...

<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>

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...

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...

This paper aims at resolving a major obstacle to practical usage of time-consistent risk-averse decision models. The recursive objective function, generally used to ensure time consistency, is complex and has no clear/direct interpretation. Practitioners rather choose a simpler and more...

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...