Conditional Distributionally Robust Functionals

This paper addresses decision making in multiple stages, where prior information is available and where consecutive and successive decisions are made. Risk measures assess the random outcome by taking various candidate probability measures into account. To justify decisions in multiple stages, it is essential to have conditional risk measures available, which respect the information, which was already revealed in the past. The paper addresses different variants of risk measures, discusses their properties in the specific context and their implications in multistage decision making. Various examples of risk measures on simple probability spaces with finite support illustrate the content. The Wasserstein and nested distance are involved to make decision making with numerous scenarios numerically tractalbe.