Related papers: The randomly distorted Choquet integrals with resp…
Considerable literature has been devoted to developing statistical inferential results for risk measures, especially for those that are of the form of L-functionals. However, practical and theoretical considerations have highlighted quite a…
We present results for Choquet integrals with minimal assumptions on the monotone set function through which they are defined. They include the equivalence of sublinearity and strong subadditivity independent of regularity assumptions on…
Linear optimization problems are investigated whose parameters are uncertain. We apply coherent distortion risk measures to capture the possible violation of a restriction. Each risk constraint induces an uncertainty set of coefficients,…
We propose a multivariate extension of a well-known characterization by S. Kusuoka of regular and coherent risk measures as maximal correlation functionals. This involves an extension of the notion of comonotonicity to random vectors…
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…
Optimization of distortion riskmetrics with distributional uncertainty has wide applications in finance and operations research. Distortion riskmetrics include many commonly applied risk measures and deviation measures, which are not…
Conformal risk control is an extension of conformal prediction for controlling risk functions beyond miscoverage. The original algorithm controls the expected value of a loss that is monotonic in a one-dimensional parameter. Here, we…
Probabilistic risk aversion, defined through quasi-convexity in probabilistic mixtures, is a common useful property in decision analysis. We study a general class of non-monotone mappings, called the generalized rank-dependent functions,…
In this paper, by proposing two new kinds of distributional uncertainty sets, we explore robustness of distortion risk measures against distributional uncertainty. To be precise, we first consider a distributional uncertainty set which is…
This paper deals with multidimensional dynamic risk measures induced by conditional $g$-expectations. A notion of multidimensional $g$-expectation is proposed to provide a multidimensional version of nonlinear expectations. By a technical…
We develop a novel stochastic valuation and premium calculation principle based on probability measure distortions that are induced by quantile processes in continuous time. Necessary and sufficient conditions are derived under which the…
We give a complete characterization of both comonotone and not comonotone coherent risk measures in the discrete finite probability space, where each outcome is equally likely. To the best of our knowledge, this is the first work that…
The preservation of stochastic orders by distortion functions has become a topic of increasing interest in the reliability analysis of coherent systems. The reason of this interest is that the reliability function of a coherent system with…
Given a submodular capacity space, we prove the uniform convergence in capacity and also the uniform convergence in the Choquet-mean of order $p\ge1$ with a quantitative estimate, of the multivariate Bernstein polynomials associated to a…
The framework of this paper is that of risk measuring under uncertainty, which is when no reference probability measure is given. To every regular convex risk measure on ${\cal C}_b(\Omega)$, we associate a unique equivalence class of…
Several objects in the Extremes literature are special instances of max-stable random sup-measures. This perspective opens connections to the theory of random sets and the theory of risk measures and makes it possible to extend…
The aggregation of individual risks in large credit and insurance portfolios is guided by diversification and the law of large numbers, which formalizes the convergence of sample averages to their means. At the same time, regulatory capital…
We provide a characterization in terms of Fatou closedness for weakly closed monotone convex sets in the space of $\mathcal{P}$-quasisure bounded random variables, where $\mathcal{P}$ is a (possibly non-dominated) class of probability…
We discuss two distinct approaches, for distorting risk measures of sums of dependent random variables, which preserve the property of coherence. The first, based on distorted expectations, operates on the survival function of the sum. The…
The ratio of the hazard functions of two populations or two strata of a single population plays an important role in time-to-event analysis. Cox regression is commonly used to estimate the hazard ratio under the assumption that it is…