While a lot of research concentrates on the respective merits of VaR and TCE, which are the two most classic risk indicators used by financial institutions, little has been written on the equivalence between such indicators. Further, TCE, despite its merits, may not be the most accurate...

In this paper, we derive upper and lower bounds on the Range Value-at-Risk of the portfolio loss when we only know its mean and variance, and its feature of unimodality. In a first step, we use some classic results on stochastic ordering to reduce this optimization problem to a parametric one,...

Robustness of risk measures to changes in underlying loss distributions (distributional uncertainty) is of crucial importance when making well-informed risk management decisions. In this paper, we quantify for any given distortion risk measure its robustness to distributional uncertainty by...

In this paper, we assess the magnitude of model uncertainty of credit risk portfolio models, i.e., what is the maximum and minimum Value-at-Risk (VaR) of a portfolio of risky loans that can be justi ed given a certain amount of available information. Puccetti and Ruschendorf (2012a) and...

The bounds for risk measures of a portfolio when its components have known marginal distributions but the dependence among the risks is unknown are often too wide to be useful in practice. Moreover, availability of additional dependence information, such as knowledge of some higher-order...

Recent literature deals with bounds on the Value-at-Risk (VaR) of risky portfolios when only the marginal distributions of the components are known. In this paper we study Value-at-Risk bounds when the variance of the portfolio sum is also known, a situation that is of considerable interest in...

The assessment of portfolio risk is often explicitly (e.g., the square root formula under Basel III) or implicitly (e.g., credit risk portfolio models) driven by the marginal distributions of the risky components and the correlations amongst them. We assess the extent by which such practice is...

In Section 2 of Bernard et al. (2020), we study bounds on Range Value-at-Risk (RVaR) under the assumption of non-negative risk. However, Proposition 3 is erroneous, and hence Theorems 3, 4, and 5 and Corollary 5 are no longer valid. In this corrigendum, we provide a direct replacement of these...

We propose a novel model-free approach for extracting the risk-neutral quantile function of an asset using options written on this asset. We develop two applications. First, we show how for a given stochastic asset model our approach makes it possible to simulate the underlying terminal asset...

We derive upper and lower bounds for the Range Value-at-Risk of a unimodal random variable under knowledge of the mean, variance, symmetry, and a possibly bounded support. Moreover, we provide a generalization of the Gauss inequality for symmetric distributions with known support