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...

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...