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 …

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 …

This paper proposes a new method to introduce coherent risk measures for risks with infinite expectation, such as those … characterized by some Pareto distributions. Extensions of the conditional value at risk, the weighted conditional value at risk and …

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 … general framework for portfolio theory of Maier-Paape and Zhu (2018), presented in Part I of this series. As an alternative to … classical portfolio risk measures such as the standard deviation, we, in particular, construct risk measures related to the …

In the present paper, we study quantile risk measures and their domain. Our starting point is that, for a probability … measure Q on the open unit interval and a wide class L Q of random variables, we define the quantile risk measure ϱ Q as the … map that integrates the quantile function of a random variable in L Q with respect to Q . The definition of L Q ensures …

risk measure and expected utility. …

Risk analysis and management currently have a strong presence in financial institutions, where high performance and … regard, we approach the estimation of the widely-employed portfolio risk metrics value-at-risk (VaR) and conditional value-at-risk … (cVaR) by means of nested Monte Carlo (MC) simulations. We do so by combining theory and software/hardware implementation …