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 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.

Sharp bounds for sums of dependent risks / Giovanni Puccetti; Ludger Rüschendorf. - In: JOURNAL OF APPLIED PROBABILITY. - ISSN 0021-9002. - STAMPA. - 50:(2013), pp. 42-53. [10.1239/jap/1363784423]

Sharp bounds for sums of dependent risks

PUCCETTI, GIOVANNI;
2013

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 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.
50
42
53
Giovanni Puccetti; Ludger Rüschendorf
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2158/796862
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