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....

The paper concerns primal and dual representations as well as time consistency of set-valued dynamic risk measures. Set-valued risk measures appear naturally when markets with transaction costs are considered and capital requirements can be made in a basket of currencies or assets. Time...

Abstract 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 are presented. These are then used to obtain the main results of this paper on time consistency;...

We quantify the sensitivity of the Eisenberg-Noe clearing vector to estimation errors in the bilateral liabilities of a financial system. The interbank liabilities matrix is a crucial input to the computation of the clearing vector. However, in practice central bankers and regulators must often...

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...