Choosing solutions under risk and uncertainty requires the consideration of several factors. One of the main factors in … choosing a solution is modeling the decision maker's attitude to risk. The expected utility theory was the first approach that … allowed to correctly model various nuances of the attitude to risk. Further research in this area has led to the emergence of …

Evaluating risk measures, premiums, and capital allocation based on dependent multi-losses is a notoriously difficult … by a heavy-tailed background risk. A particular attention is given to the distortion and weighted risk measures and … allocations, as well as their special cases such as the conditional layer expectation, tail value at risk, and the truncated tail …

risk measure and expected utility. …

framework is model-free and allows for stresses on the output such as (a) the mean and variance, (b) any distortion risk measure … including the Value-at-Risk and Expected-Shortfall, and (c) expected utility type constraints, thus making the reverse … sensitivity analysis framework suitable for risk models. …

distribution, may contain more than one parameter. The coherency of the resulting risk measures is ensured by restricting the … exponentiated exponential and Gompertz distributions. Closed-form expressions for risk measures were derived for uniform … risk measures. We then propose a simple plug-in estimate of risk measures and conduct simulation studies to compare and …

distortion parameters can be influenced by political factors or users' risk aversion levels, we generate plots of the distortion … functions to examine how these parameters impact the tasks and users' attitudes toward risk. The coherent properties of the … resulting risk measures are explored, outlining the conditions under which the transmuted Kumaraswamy and transmuted truncated …

When the uni-variate risk measure analysis is generalized into the multi-variate setting, many complex theoretical and … applied problems arise, and therefore the mathematical models used for risk quantification usually present model risk. As a … task, we propose a novel multi-variate risk measure, based on the notion of the Wasserstein barycenter. The proposed …

measures of risk. Furthermore, Qα(X ; p) is the optimal value in a certain minimization problem, the minimizers in which are … problems. In finance, Q0(X;p) and Q1(X ; p) are known as the value at risk (VaR) and the conditional value at risk (CVaR). The … sensitivity to risk. The problems of the effective computation of the bounds are considered. Various other related results are …

This article reviews two leading measures of financial risk and an emerging alternative. Embraced by the Basel accords …, value-at-risk and expected shortfall are the leading measures of financial risk. Expectiles offset the weaknesses of value-at-risk … (VaR) and expected shortfall. Indeed, expectiles are the only elicitable law-invariant coherent risk measures. After …

The aim of this paper is to provide several examples of convex risk measures necessary for the application of the … classical portfolio risk measures such as the standard deviation, we, in particular, construct risk measures related to the … and Mahmoud (2017), and Zabarankin, Pavlikov, and Uryasev (2014), who used the absolute drawdown, our risk measure is …