Related papers: A Remark on the Structure of Expectiles
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 introduce and study the main properties of a class of convex risk measures that refine Expected Shortfall by simultaneously controlling the expected losses associated with different portions of the tail distribution. The corresponding…
We propose a general approach for supervised learning with structured output spaces, such as combinatorial and polyhedral sets, that is based on minimizing estimated conditional risk functions. Given a loss function defined over pairs of…
Recently defined expectile regions capture the idea of centrality with respect to a multivariate distribution, but fail to describe the tail behavior while it is not at all clear what should be understood by a tail of a multivariate…
A generalization of expectiles for d-dimensional multivariate distribution functions is introduced. The resulting geometric expectiles are unique solutions to a convex risk minimization problem and are given by d-dimensional vectors. They…
Obtaining guarantees on the convergence of the minimizers of empirical risks to the ones of the true risk is a fundamental matter in statistical learning. Instead of deriving guarantees on the usual estimation error, the goal of this paper…
The conventional definition of extremality of a finite collection of sets is extended by replacing a fixed point (extremal point) in the intersection of the sets by a collection of sequences of points in the individual sets with the…
We address the problem that classical risk measures may not detect the tail risk adequately. This can occur for instance due to averaging when calculating the Expected Shortfall. The current literature proposes the so-called adjusted…
We provide a constructive way of defining new elicitable risk measures that are characterised by a multiplicative scoring function. We show that depending on the choice of the scoring function's components, the resulting risk measure…
The present article is devoted to the semi-parametric estimation of multivariate expectiles for extreme levels. The considered multivariate risk measures also include the possible conditioning with respect to a functional covariate,…
The standard coherence criterion for lower previsions is expressed using an infinite number of linear constraints. For lower previsions that are essentially defined on some finite set of gambles on a finite possibility space, we present a…
Predictions of hydrological models should be probabilistic in nature. Our aim is to introduce a method that estimates directly the uncertainty of hydrological simulations using expectiles, thus complementing previous quantile-based direct…
We consider the worst-case expectation of a permutation invariant ambiguity set of discrete distributions as a proxy-cost for data-driven expected risk minimization. For this framework, we coin the term ordered risk minimization to…
Systemic risk measures play a crucial role in analyzing individual losses conditional on extreme system-wide disasters. In this paper, we provide a unified asymptotic treatment for systemic risk measures. First, we classify them into two…
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…
As a counterpart to the (static) risk measures of generalized quantiles and motivated by Bellini et al. (2018), we propose a new kind of conditional risk measure called conditional generalized quantiles. We first show their well-definedness…
The issue related to the quantification of the tail risk of cryptocurrencies is considered in this paper. The statistical methods used in the study are those concerning recent developments in Extreme Value Theory (EVT) for weakly dependent…
Marginal expected shortfall is unquestionably one of the most popular systemic risk measures. Studying its extreme behaviour is particularly relevant for risk protection against severe global financial market downturns. In this context,…
In the context of Structural Risk Minimization, one is presented a sequence of classes $\{\mathcal{G}_j\}$ from which, given a random sample $(X_i,Y_i)$ one wants to choose a strongly consistent estimator. For certain types of classes of…
The attributable risk, often called the population attributable risk, is in many epidemiological contexts a more relevant measure of exposure-disease association than the excess risk, relative risk, or odds ratio. When estimating…