Worst VaR scenarios: A remark

Theorem 15 of Embrechts et al. [Embrechts, Paul, Höing, Andrea, Puccetti, Giovanni, 2005. Worst VaR scenarios. Insurance: Math. Econom. 37, 115-134] proves that comonotonicity gives rise to the on-average-most-adverse Value-at-Risk scenario for a function of dependent risks, when the marginal distributions are known but the dependence structure between the risks is unknown. This note extends this result to the case where, rather than no information, partial information is available on the dependence structure between the risks. A result of Kaas et al. [Kaas, Rob, Dhaene, Jan, Goovaerts, Marc J., 2000. Upper and lower bounds for sums of random variables. Insurance: Math. Econom. 23, 151-168] is also generalized for this purpose.