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Bounds for Functions of Multivariate Risks

by Paul Embrechts of ETH Zurich, and
Giovanni Puccetti of the University of Firenze

April 4, 2005

Abstract: Li, Scarsini, and Shaked (1996a) provide bounds on the distribution and the tail for functions of dependent random vectors having fixed multivariate marginals. In this paper, we correct a result stated in the above article and we give improved bounds in the case of the sum of identically distributed random vectors. Moreover, we provide the dependence structures meeting the bounds when the fixed marginals are uniformly distributed on the k-dimensional hypercube. Finally, a definition of a multivariate risk measure is given along with actuarial/financial applications.

AMS Classification: 60E15, 60E05.

Keywords: multivariate marginals, coupling, dual bounds, Value-at-Risk, risk measures.

Published in: Journal of Multivariate Analysis, Vol. 97, No. 2, (February 2006), pp. 526-547.

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Related reading: Bounds for Functions of Dependent Risks