Recent developments in set optimization are surveyed and extended including various set
relations as well as fundamental constructions of a convex analysis for set-and vector …

Since risky positions in multivariate portfolios can be offset by various choices of capital
requirements that depend on the exchange rules and related transaction costs, it is natural …

In this paper, we investigate the fair valuation of insurance liabilities in a dynamic multi-
period setting. We define a fair dynamic valuation as a valuation which is actuarial (mark-to …

Building upon the dynamic programming principle for set valued functions arising from many
applications, in this paper we propose a new notion of set valued PDEs. The key component …

We investigate to which extent the relevant features of (static) Systemic Risk Measures can
be extended to a conditional setting. After providing a general dual representation result, we …

In this work we give a comprehensive overview of the time consistency property of dynamic
risk and performance measures, focusing on a the discrete time setup. The two key …

Set-valued dynamic risk measures are defined on with and with an image space in the
power set of. Primal and dual representations of dynamic risk measures are deduced …

A method for calculating multi-portfolio time consistent multivariate risk measures in discrete
time is presented. Market models for d assets with transaction costs or illiquidity and …

Hedging techniques have been widely adopted in market-consistent or fair valuation
approach required by recent solvency regulations, to take into account the market prices of …

Risk measures for multivariate financial positions are studied in a utility-based framework.
Under a certain incomplete preference relation, shortfall and divergence risk measures are …