Related papers: Eliciting reference measures of law-invariant func…
Invariant Causal Prediction (Peters et al., 2016) is a technique for out-of-distribution generalization which assumes that some aspects of the data distribution vary across the training set but that the underlying causal mechanisms remain…
Our paper contributes to the theory of conditional risk measures and conditional certainty equivalents. We adopt a random modular approach which proved to be effective in the study of modular convex analysis and conditional risk measures.…
Motivated by optimal investment problems in mathematical finance, we consider a variational problem of Neyman-Pearson type for law-invariant robust utility functionals and convex risk measures. Explicit solutions are found for…
Identification and scoring functions are statistical tools to assess the calibration and the relative performance of risk measure estimates, e.g., in backtesting. A risk measures is called identifiable (elicitable) it it admits a strict…
The angular measure on the unit sphere characterizes the first-order dependence structure of the components of a random vector in extreme regions and is defined in terms of standardized margins. Its statistical recovery is an important step…
We introduce the formalism of generalized Fourier transforms in the context of risk management. We develop a general framework to efficiently compute the most popular risk measures, Value-at-Risk and Expected Shortfall (also known as…
We derive an efficient stochastic algorithm for inverse problems that present an unknown linear forcing term and a set of nonlinear parameters to be recovered. It is assumed that the data is noisy and that the linear part of the problem is…
A causal set is a partially ordered set on a countably infinite ground-set such that each element is above finitely many others. A natural extension of a causal set is an enumeration of its elements which respects the order. We bring…
Probability density functions (PDFs) can be understood as continuous compositions by the theory of Bayes spaces. The origin of a Bayes space is determined by a given reference measure. This can be easily changed through the well-known chain…
We propose a generalization of the classical notion of the $V@R_{\lambda}$ that takes into account not only the probability of the losses, but the balance between such probability and the amount of the loss. This is obtained by defining a…
Consider an ergodic stationary random field $A$ on the ambient space $\mathbb R^d$. In order to establish concentration properties for nonlinear functions $Z(A)$, it is standard to appeal to functional inequalities like Poincar\'e or…
We place ourselves in a functional regression setting and propose a novel methodology for regressing a real output on vector-valued functional covariates. This methodology is based on the notion of signature, which is a representation of a…
Distributionally robust optimization involves various probability measures in its problem formulation. They can be bundled to constitute a risk functional. For this equivalence, risk functionals constitute a fundamental building block in…
Expectiles were introduced by Newey and Powell (1987) in the context of linear regression models. Recently, Bellini et al. (2014) revealed that expectiles can also be seen as reasonable law-invariant risk measures. In this article, we show…
Static analysers search for overapproximating proofs of safety commonly known as safety invariants. Fundamentally, such analysers summarise traces into sets of states, thus trading the ability to distinguish traces for computational…
Sequential estimation of the success probability $p$ in inverse binomial sampling is considered in this paper. For any estimator $\hat p$, its quality is measured by the risk associated with normalized loss functions of linear-linear or…
The regulator is interested in proposing a capital adequacy test by specifying an acceptance set for firms' capital positions at the end of a given period. This set needs to be surplus-invariant, i.e., not to depend on the surplus of firms'…
We consider debiased inference on finite-dimensional functionals of infinite-dimensional least-squares solutions to inverse problems as a way to avoid having to assume exact solutions exist. Such assumptions are substantive and not…
Building on recent results regarding symmetric probabilistic constructions of countable structures, we provide a method for constructing probability measures, concentrated on certain classes of countably infinite structures, that are…
By means of the techniques of Boolean valued analysis, we provide a transfer principle between duality theory of classical convex risk measures and duality theory of conditional risk measures. Namely, a conditional risk measure can be…