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The robustness of risk measures to changes in underlying loss distributions (distributional uncertainty) is of crucial importance in making well-informed decisions. In this paper, we quantify, for the class of distortion risk measures with…
We discuss equivalent axiomatic characterizations of distortion risk measures, and give a novel and concise proof of the characterization of elicitable distortion risk measures. Elicitability has recently been discussed as a desirable…
Model uncertainty has been one prominent issue both in the theory of risk measures and in practice such as financial risk management and regulation. Motivated by this observation, in this paper, we take a new perspective to describe the…
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…
In this paper, we introduce the rich classes of conditional distortion (CoD) risk measures and distortion risk contribution ($\Delta$CoD) measures as measures of systemic risk and analyze their properties and representations. The classes…
Risk measures connect probability theory or statistics to optimization, particularly to convex optimization. They are nowadays standard in applications of finance and in insurance involving risk aversion. This paper investigates a wide…
The paper investigates the robust distortion risk measure with linear penalty function under distribution uncertainty. The distribution uncertainties are characterized by predetermined moment conditions or constraints on the Wasserstein…
We establish sharp upper and lower bounds for distortion risk metrics under distributional uncertainty. The uncertainty sets are characterized by four key features of the underlying distribution: mean, variance, unimodality, and Wasserstein…
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…
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…
We study randomly distorted Choquet integrals with respect to a capacity c on a measurable space ({\Omega},F), where the capacity c is distorted by a G-measurable random distortion function (with G a sub-{\sigma}-algebra of F). We establish…
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…
In this paper, we will show that under certain conditions, associated to any fixed distortion function $g$, the distortion risk measure of a sum of two counter-monotonic risks can be expressed as the sum of two related distortion risk…
We study risk sharing among agents with preferences modeled by heterogeneous distortion risk measures, who are not necessarily risk averse. Pareto optimality for agents using risk measures is often studied through the lens of…
Distortion risk measures are extensively used in finance and insurance applications because of their appealing properties. We present three methods to construct new class of distortion functions and measures. The approach involves 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…
Geometrically convex functions constitute an interesting class of functions obtained by replacing the arithmetic mean with the geometric mean in the definition of convexity. As recently suggested, geometric convexity may be a sensible…
In this paper, we consider the problem of optimal reinsurance design, when the risk is measured by a distortion risk measure and the premium is given by a distortion risk premium. First, we show how the optimal reinsurance design for the…
We extend the scope of risk measures for which backtesting models are available by proposing a multinomial backtesting method for general distortion risk measures. The method relies on a stratification and randomization of risk levels. We…
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…