Related papers: Central limit theorems for vector-valued composite…
Max-stable random fields are very appropriate for the statistical modelling of spatial extremes. Hence, integrals of functions of max-stable random fields over a given region can play a key role in the assessment of the risk of natural…
We study combinations of risk measures under no restrictive assumption on the set of alternatives. We develop and discuss results regarding the preservation of properties and acceptance sets for the combinations of risk measures. One of the…
In this paper, we discuss the joint value distribution of $L$-functions in a suitable class. We obtain joint large deviations results in the central limit theorem for these $L$-functions and some mean value theorems, which give evidence…
We investigate the modeling and the numerical solution of machine learning problems with prediction functions which are linear combinations of elements of a possibly infinite-dimensional dictionary. We propose a novel flexible composite…
Accretive and monotone operator theory are central branches of nonlinear functional analysis and constitute the abstract study of set-valued mappings between function spaces. This paper deals with the computational properties of certain…
The relationship between set-valued risk measures for processes and vectors on the optional filtration is investigated. The equivalence of risk measures for processes and vectors and the equivalence of their penalty function formulations…
We estimate linear functionals in the classical deconvolution problem by kernel estimators. We obtain a uniform central limit theorem with $\sqrt{n}$-rate on the assumption that the smoothness of the functionals is larger than the…
We provide an abstract multivariate central limit theorem with the Lindeberg-type error bounded in terms of Lipschitz functions (Wasserstein 1-distance) or functions with bounded second or third derivatives. The result is proved by means of…
In this work we propose deep learning-based algorithms for the computation of systemic shortfall risk measures defined via multivariate utility functions. We discuss the key related theoretical aspects, with a particular focus on the…
We consider noisy non-synchronous discrete observations of a continuous semimartingale with random volatility. Functional stable central limit theorems are established under high-frequency asymptotics in three setups: one-dimensional for…
We establish a profound connection between coherent risk measures, a prominent object in quantitative finance, and uniform integrability, a fundamental concept in probability theory. Instead of working with absolute values of random…
A general lower bound is developed for the minimax risk when estimating an arbitrary functional. The bound is based on testing two composite hypotheses and is shown to be effective in estimating the nonsmooth functional…
In multi-task learning several related tasks are considered simultaneously, with the hope that by an appropriate sharing of information across tasks, each task may benefit from the others. In the context of learning linear functions 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…
Functional linear regression analysis aims to model regression relations which include a functional predictor. The analog of the regression parameter vector or matrix in conventional multivariate or multiple-response linear regression…
In this paper, we investigate the functional central limit theorem for stochastic processes associated to partial sums of additive functionals of reversible Markov chains with general spate space, under the normalization standard deviation…
In many sequential decision-making problems we may want to manage risk by minimizing some measure of variability in costs in addition to minimizing a standard criterion. Conditional value-at-risk (CVaR) is a relatively new risk measure that…
We axiomatically introduce risk-consistent conditional systemic risk measures defined on multidimensional risks. This class consists of those conditional systemic risk measures which can be decomposed into a state-wise conditional…
We develop a new classification framework based on the theory of coherent risk measures and systemic risk. The proposed approach is suitable for multi-class problems when the data is noisy, scarce (relative to the dimension of the problem),…
We conduct a non asymptotic study of the Cross Validation (CV) estimate of the generalization risk for learning algorithms dedicated to extreme regions of the covariates space. In this Extreme Value Analysis context, the risk function…