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....

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...

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>

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...

We develop a novel framework for computing the total valuation adjustment (XVA) of a European claim accounting for funding costs, counterparty credit risk, and collateralization. Based on no-arbitrage arguments, we derive the nonlinear backward stochastic differential equations (BSDEs)...

We study the semilinear partial differential equation (PDE) associated with the non-linear BSDE characterizing buyer's and seller's XVA in a framework that allows for asymmetries in funding, repo and collateral rates, as well as for early contract termination due to counterparty credit risk. We...

Two major financial market complexities are transaction costs and uncertain volatility, and we analyze their joint impact on the problem of portfolio optimization. When volatility is constant, the transaction costs optimal investment problem has a long history, especially in the use of...

<Para ID="Par1">We price a contingent claim liability (claim for short) using a utility indifference argument. We consider an agent with exponential utility, who invests in a stock and a money market account with the goal of maximizing the utility of his investment at the final time T in the presence of a...</para>