Related papers: On evaluation of joint risk for non-negative multi…
In many practical applications, evaluating the joint impact of combinations of environmental variables is important for risk management and structural design analysis. When such variables are considered simultaneously, non-stationarity can…
Risk measure forecast and model have been developed in order to not only provide better forecast but also preserve its (empirical) property especially coherent property. Whilst the widely used risk measure of Value-at-Risk (VaR) has shown…
In this paper, we introduce two alternative extensions of the classical univariate Value-at-Risk (VaR) in a multivariate setting. The two proposed multivariate VaR are vector-valued measures with the same dimension as the underlying risk…
We establish the first axiomatic theory for diversification indices using six intuitive axioms: non-negativity, location invariance, scale invariance, rationality, normalization, and continuity. The unique class of indices satisfying these…
This paper is devoted to the introduction and study of a new family of multivariate elicitable risk measures. We call the obtained vector-valued measures multivariate expectiles. We present the different approaches used to construct our…
In economics, insurance and finance, value at risk (VaR) is a widely used measure of the risk of loss on a specific portfolio of financial assets. For a given portfolio, time horizon, and probability $\alpha$, the $100\alpha\%$ VaR is…
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…
Distance multivariance is a multivariate dependence measure, which can detect dependencies between an arbitrary number of random vectors each of which can have a distinct dimension. Here we discuss several new aspects, present a concise…
We establish a connection between dependence structures and subclasses of distortion riskmetrics under which the latter are additive. A new notion of positive dependence, called partial comonotonicity, is developed, which nests the existing…
It has been proposed that complex populations, such as those that arise in genomics studies, may exhibit dependencies among observations as well as among variables. This gives rise to the challenging problem of analyzing unreplicated…
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…
The intuition of risk is based on two main concepts: loss and variability. In this paper, we present a composition of risk and deviation measures, which contemplate these two concepts. Based on the proposed Limitedness axiom, we prove that…
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…
Managers, employers, policymakers, and others often seek to understand whether decisions are biased against certain groups. One popular analytic strategy is to estimate disparities after adjusting for observed covariates, typically with a…
This work is devoted to the development of a distributionally robust active fault diagnosis approach for a class of nonlinear systems, which takes into account any ambiguity in distribution information of the uncertain model parameters.…
Risk measures for multivariate financial positions are studied in a utility-based framework. Under a certain incomplete preference relation, shortfall and divergence risk measures are defined as the optimal values of specific set…
Diagnostic test accuracy studies observe the result of a gold standard procedure that defines the presence or absence of a disease and the result of a diagnostic test. They typically report the number of true positives, false positives,…
We propose and axiomatize preferences on a product state space in light of uncertainty regarding the dependency of different payoff-relevant factors. Dependence structures allow to decompose probabilities and allow to pin down behavior…
We quantify model risk of a financial portfolio whereby a multi-period mean-standard-deviation criterion is used as a selection criterion. In this work, model risk is defined as the loss due to uncertainty of the underlying distribution of…
We consider settings in which the distribution of a multivariate random variable is partly ambiguous. We assume the ambiguity lies on the level of the dependence structure, and that the marginal distributions are known. Furthermore, a…