Embrechts, Paul, Andrea Höing, Giovanni Puccetti, "Worst VaR Scenarios", Insurance: Mathematics and Economics, Vol. 37, No. 1, (August 2005), pp. 115-134.
Abstract: The worst possible Value-at-Risk for a non-decreasing function ψ of n dependent risks is known when n = 2 or the copula of the portfolio is bounded from below. In this paper we analyze the properties of the dependence structures leading to this solution, in particular their form and the implied functional dependence between the marginals. Furthermore, we criticise the assumption of the worst possible scenario for VaR-based risk management and we provide an alternative approach supporting comonotonicity.
Keywords: Value-at-Risk, Dependent risks, Copulas, Comonotonic risks.