Abstract: Li et al. [Distributions with Fixed Marginals and Related Topics, vol. 28, Institute of Mathematics and Statistics, Hayward, CA, 1996, pp. 198–212] provide bounds on the distribution and on 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.

Bounds for Functions of Multivariate Risks / PAUL EMBRECHTS; G. PUCCETTI. - In: JOURNAL OF MULTIVARIATE ANALYSIS. - ISSN 0047-259X. - ELETTRONICO. - 97:(2006), pp. 526-547. [10.1016/j.jmva.2005.04.001]

### Bounds for Functions of Multivariate Risks

#### Abstract

Abstract: Li et al. [Distributions with Fixed Marginals and Related Topics, vol. 28, Institute of Mathematics and Statistics, Hayward, CA, 1996, pp. 198–212] provide bounds on the distribution and on 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.
##### Scheda breve Scheda completa Scheda completa (DC)
2006
97
526
547
PAUL EMBRECHTS; G. PUCCETTI
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Utilizza questo identificatore per citare o creare un link a questa risorsa: `https://hdl.handle.net/2158/218260`