Related papers: Surplus-invariant risk measures
The financial crisis has dramatically demonstrated that the traditional approach to apply univariate monetary risk measures to single institutions does not capture sufficiently the perilous systemic risk that is generated by the…
Latent space models have been widely adopted in modeling network data. Developing statistical inference for estimated model parameters enables quantifying associated uncertainty and is pivotal for downstream tasks. Despite recent progress…
Optimization of conditional convex risk measure is a central theme in dynamic portfolio selection theory, which has not yet systematically studied in the previous literature perhaps since conditional convex risk measures are neither random…
A risk analyst assesses potential financial losses based on multiple sources of information. Often, the assessment does not only depend on the specification of the loss random variable but also various economic scenarios. Motivated by this…
We discuss recent work for causal inference and predictive robustness in a unifying way. The key idea relies on a notion of probabilistic invariance or stability: it opens up new insights for formulating causality as a certain risk…
Scale invariance is a central organizing principle in physics, underlying phenomena that range from critical behaviour in statistical mechanics to transport and chaos in nonlinear dynamical systems. Here we present a unified and physically…
Model sets (also called cut and project sets) are generalizations of lattices. Here we show how the self-similarities of model sets are a natural replacement for the group of translations of a lattice. This leads us to the concept of…
In Basili and Pratelli (2024), a novel and coherent concept of interval probability measures has been introduced, providing a method for representing imprecise probabilities and uncertainty. Within the framework of set algebra, we…
Previous derivations of the sum and product rules of probability theory relied on the algebraic properties of Boolean logic. Here they are derived within a more general framework based on lattice theory. The result is a new foundation of…
Emergent patterns in complex systems are related to many intriguing phenomena in modern science and philosophy. Several conceptions such as weak, strong and robust emergence have been proposed to emphasize different epistemological and…
Higher order risk measures are stochastic optimization problems by design, and for this reason they enjoy valuable properties in optimization under uncertainties. They nicely integrate with stochastic optimization problems, as has been…
This paper introduces a novel robust trading paradigm, called \textit{multi-double linear policies}, situated within a \textit{generalized} lattice market. Distinctively, our framework departs from most existing robust trading strategies,…
The concept of convex compactness, weaker than the classical notion of compactness, is introduced and discussed. It is shown that a large class of convex subsets of topological vector spaces shares this property and that is can be used in…
This paper studies distributionally robust optimization for a rich class of risk measures with ambiguity sets defined by $\phi$-divergences. The risk measures are allowed to be non-linear in probabilities, are represented by Choquet…
This paper proposes a general framework for inference on three types of almost dominances: almost Lorenz dominance, almost inverse stochastic dominance, and almost stochastic dominance. We first generalize almost Lorenz dominance to almost…
For more than half a century lattices in Lie groups played an important role in geometry, number theory and group theory. Recently the notion of Invariant Random Subgroups (IRS) emerged as a natural generalization of lattices. It is thus…
We introduce two kinds of risk measures with respect to some reference probability measure, which both allow for a certain order structure and domination property. Analyzing their relation to each other leads to the question when a certain…
This paper introduces a novel concept of interval probability measures that enables the representation of imprecise probabilities, or uncertainty, in a natural and coherent manner. Within an algebra of sets, we introduce a notion of weak…
Consider the problem of learning a large number of response functions simultaneously based on the same input variables. The training data consist of a single independent random sample of the input variables drawn from a common distribution…
In this work we develop a re-formulation of quantum field theory through the more general weighted Lorentz invariant measures that the definition of quantum fields allows; this approach provides finite answers for the long-live problems of…