The nested distance, also process distance, provides a quantitative measure of distance for stochastic processes. It is the crucial and determining distance for stochastic optimization problems.In this paper we demonstrate ...

We provide a new identity for the multistage Average Value-at-Risk. The identity is based on the conditional Average Value-at-Risk at random level, which is introduced. It is of interest in situations, where the information ...

This paper considers distributionally robust formulations of a two stage stochastic programmingproblem with the objective of minimizing a distortion risk of the minimal cost incurred at the secondstage.We carry out stability ...

Risk measures, or coherent measures of risk are often considered on the space $L^\infty$, andimportant theorems on risk measures build on that space. Other risk measures, among themthe most important risk measure – the ...