We specify a general methodological framework for systemic risk measures via
multidimensional acceptance sets and aggregation functions. Existing systemic risk …

We provide a dual representation of quasi-convex maps π:L_F%→L_G, between two locally
convex lattices of random variables, in terms of conditional expectations. This generalizes …

The concepts of a conditional set, a conditional inclusion relation and a conditional
Cartesian product are introduced. The resulting conditional set theory is sufficiently rich in …

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 …

Recently, based on the idea of randomizing space theory, random convex analysis has
been being developed in order to deal with the corresponding problems in random …

Recently, several authors focused their attention on acceptability indexes (AI) and their
applications in Finance. The AI notion turns out to be quite flexible and several applications …

First, this paper introduces the notion of L 0-convex compactness for a special class of
closed convex subsets–closed L 0-convex subsets of a Hausdorff topological module over …

Evenly convex sets in a topological vector space are defined as the intersection of a family of
open half spaces. We introduce a generalization of this concept in the conditional framework …

Several results in functional analysis are extended to the setting of $ L^ 0$-modules, where
$ L^ 0$ denotes the ring of all measurable functions $ x\colon\Omega\to\mathbb {R} $. The …