Related papers: Comonotonic measures of multivariate risks
We give an axiomatic framework for conditional generalized deviation measures. Under financially reasonable assumptions, we give the correspondence between conditional coherent risk measures and generalized deviation measures. Moreover, we…
We consider the optimal mass transportation problem in $\RR^d$ with measurably parameterized marginals, for general cost functions and under conditions ensuring the existence of a unique optimal transport map. We prove a joint measurability…
We study the problem of maximizing a spectral risk measure of a given output function which depends on several underlying variables, whose individual distributions are known but whose joint distribution is not. We establish and exploit an…
In this paper, we study dependence uncertainty and the resulting effects on tail risk measures, which play a fundamental role in modern risk management. We introduce the notion of a regular dependence measure, defined on multi-marginal…
In this paper, we want to establish some general results in the Lorentzian optimal transport theory that have well-known Riemannian counterparts. As a first result, we will provide non-trivial assumptions on the measures to ensure strong…
In [16], a new family of vector-valued risk measures called multivariate expectiles is introduced. In this paper, we focus on the asymptotic behavior of these measures in a multivariate regular variations context. For models with equivalent…
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…
In this paper we consider the axiomatic characterization of information and certainty measures in a unified way. We present the general axiomatic system which captures the common properties of a large number of the measures previously…
A.N. Kolmogorov proposed several problems on stochastic processes, which has been rarely addressed later on. One of the open problems are stochastic processes with discontinuous covariance function. For example, semicontinuous covariance…
Measuring the correlation (association) between two random variables is one of the important goals in statistical applications. In the literature, the covariance between two random variables is a widely used criterion in measuring the…
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…
Regression analysis under the assumption of monotonicity is a well-studied statistical problem and has been used in a wide range of applications. However, there remains a lack of a broadly applicable methodology that permits information…
When estimating the risk of a P&L from historical data or Monte Carlo simulation, the robustness of the estimate is important. We argue here that Hampel's classical notion of qualitative robustness is not suitable for risk measurement and…
This survey explores the foundational theory and recent developments in the study of hyperuniformity. We present a comprehensive mathematical framework in the context of weakly stationary random measures, emphasizing spectral…
We study dynamic risk measures in a very general framework enabling to model uncertainty and processes with jumps. We previously showed the existence of a canonical equivalence class of probability measures hidden behind a given set of…
In this paper, an optimization problem with uncertain constraint coefficients is considered. Possibility theory is used to model the uncertainty. Namely, a joint possibility distribution in constraint coefficient realizations, called…
In this paper we study optimal stopping problems with respect to distorted expectations of the form \begin{eqnarray*} \mathcal{E}(X)=\int_{-\infty}^{\infty} x\,dG(F_X(x)), \end{eqnarray*} where $F_X$ is the distribution function of $X$ and…
In this paper, we propose a new test for the equality of several covariance functions for functional data. Its test statistic is taken as the supremum value of the sum of the squared differences between the estimated individual covariance…
We introduce set risk measures (SRMs), real-valued maps defined on the family of non-empty closed bounded sets of essentially bounded random variables. SRMs extend traditional scalar risk measures by assigning a single capital requirement…
Multivariate spatial field data are increasingly common and whose modeling typically relies on building cross-covariance functions to describe cross-process relationships. An alternative viewpoint is to model the matrix of spectral…