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Byline: Roger J.A. Laeven
Theorem 15 of Embrechts et al. [Embrechts, Paul, Hoing, 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.
Tilburg University and CentER, Department of Econometrics and
Operations Research, P.O. Box 90153, 5000 LE Tilburg, The Netherlands
Received 15 December 2005; Revised 24 October 2008; Accepted 24