rejected, since a subadditive risk measure, by definition, cannot account for such increased risks. …This paper provides a critical analysis of the subadditivity axiom, which is the key condition for coherent risk … measures. Contrary to the subadditivity assumption, bank mergers can create extra risk. We begin with an analysis how a merger …

In this paper, the generalized Pareto distribution (GPD) copula approach is utilized to solve the conditional value-at-risk …-parametric kernel-smoothed interior and the parametric Pareto upper tail and (iii) Value-at-Risk (VaR) to quantify risk measure. The … minimizing CVaR measure and simulated copula returns combined outperforms the risk/return of domestic portfolios, such as the US …

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 …

the risk of extreme events since they appear as a natural extension of multivariate extreme-value theory to the level of …An accurate assessment of the risk of extreme environmental events is of great importance for populations, authorities … and the banking/insurance/reinsurance industry. Koch (2017) introduced a notion of spatial risk measure and a …

In this paper, we develop a framework for measuring, allocating and managing systemic risk. SystRisk, our measure of … total systemic risk, captures the a priori cost to society for providing tail-risk insurance to the financial system. Our … allocation principle distributes the total systemic risk among individual institutions according to their size-shifted marginal …

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 …

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 …