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March 2013 Sharp bounds for sums of dependent risks
Giovanni Puccetti, Ludger Rüschendorf
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J. Appl. Probab. 50(1): 42-53 (March 2013). DOI: 10.1239/jap/1363784423

Abstract

Sharp tail bounds for the sum of d random variables with given marginal distributions and arbitrary dependence structure have been known since Makarov (1981) and Rüschendorf (1982) for d=2 and, in some examples, for d≥3. Based on a duality result, dual bounds have been introduced in Embrechts and Puccetti (2006b). In the homogeneous case,\break $F1=···=Fn, with monotone density, sharp tail bounds were recently found in Wang and Wang (2011). In this paper we establish the sharpness of the dual bounds in the homogeneous case under general conditions which include, in particular, the case of monotone densities and concave densities. We derive the corresponding optimal couplings and also give an effective method to calculate the sharp bounds.

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Giovanni Puccetti. Ludger Rüschendorf. "Sharp bounds for sums of dependent risks." J. Appl. Probab. 50 (1) 42 - 53, March 2013. https://doi.org/10.1239/jap/1363784423

Information

Published: March 2013
First available in Project Euclid: 20 March 2013

zbMATH: 1282.60017
MathSciNet: MR3076771
Digital Object Identifier: 10.1239/jap/1363784423

Subjects:
Primary: 60E05, 91B30

Rights: Copyright © 2013 Applied Probability Trust

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Vol.50 • No. 1 • March 2013
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