Related papers: Set risk measures
In this paper, we study general monetary risk measures (without any convexity or weak convexity). A monetary (respectively, positively homogeneous) risk measure can be characterized as the lower envelope of a family of convex (respectively,…
In this paper, we study properties of certain risk measures associated with acceptance sets. These sets describe regulatory preconditions that have to be fulfilled by financial institutions to pass a given acceptance test. If the financial…
This paper develops an axiomatic framework for ranking metrics, a general class of functionals for evaluating and ordering financial or insurance positions. Unlike traditional risk-adjusted performance measures-such as the Sharpe ratio,…
This survey gives an introduction to monetary measures of risk as monotone and cash additive functions on spaces of univariate random variables. Primal and dual representation results as well as several examples are discussed. Principal…
Spectral risk measures (SRMs) belong to the family of coherent risk measures. A natural estimator for the class of SRMs has the form of L-statistics. Various authors have studied and derived the asymptotic properties of the empirical…
Spectral risk measures (SRMs) are risk measures that take account of user riskaversion, but to date there has been little guidance on the choice of utility function underlying them. This paper addresses this issue by examining alternative…
This paper investigates the convergence properties of sample-average approximations (SAA) for set-valued systemic risk measures. We assume that the systemic risk measure is defined using a general aggregation function with some continuity…
We provide a characterization of the realisable set covariograms, bringing a rigorous yet abstract solution to the $S\_2$ problem in materials science. Our method is based on the covariogram functional for random mesurable sets (RAMS) and…
In this paper we introduce a generalization of classical risk measures in which the risk is represented by a step function taking two values, corresponding to two endogenously determined market regimes. This extends the traditional…
The risk of financial positions is measured by the minimum amount of capital to raise and invest in eligible portfolios of traded assets in order to meet a prescribed acceptability constraint. We investigate nondegeneracy, finiteness and…
We establish a variety of numerical representations of preference relations induced by set-valued risk measures. Because of the general incompleteness of such preferences, we have to deal with multi-utility representations. We look for…
This paper introduces and fully characterizes the novel class of quasi-logconvex measures of risk, to stand on equal footing with the rich class of quasi-convex measures of risk. Quasi-logconvex risk measures naturally generalize logconvex…
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…
Mean-deviation models, along with the existing theory of coherent risk measures, are well studied in the literature. In this paper, we characterize monotonic mean-deviation (risk) measures from a general mean-deviation model by applying a…
We establish dual representations for systemic risk measures based on acceptance sets in a general setting. We deal with systemic risk measures of both "first allocate, then aggregate" and "first aggregate, then allocate" type. In both…
Despite their numerous successes, there are many scenarios where adversarial risk metrics do not provide an appropriate measure of robustness. For example, test-time perturbations may occur in a probabilistic manner rather than being…
In this research, starting from a widely accepted definition of risk, we support the idea that risk reduction is a more realistic objective than risk minimization, which represents a theoretical utopia. Furthermore, significant risk…
This paper approaches the definition and properties of dynamic convex risk measures through the notion of a family of concave valuation operators satisfying certain simple and credible axioms. Exploring these in the simplest context of a…
We present simple general conditions on the acceptance sets under which their induced monetary risk and deviation measures are comonotonic additive. We show that acceptance sets induce comonotonic additive risk measures if and only if the…
The paper concerns primal and dual representations as well as time consistency of set-valued dynamic risk measures. Set-valued risk measures appear naturally when markets with transaction costs are considered and capital requirements can be…