On the distribution of the (un)bounded sum of random variables

Umberto Cherubini, Sabrina Mulinacci and Silvia Romagnoli

Insurance: Mathematics and Economics, 2011, vol. 48, issue 1, pages 56-63

Abstract: We propose a general treatment of random variables aggregation accounting for the dependence among variables and bounded or unbounded support of their sum. The approach is based on the extension to the concept of convolution to dependent variables, involving copula functions. We show that some classes of copula functions (such as Marshall-Olkin and elliptical) cannot be used to represent the dependence structure of two variables whose sum is bounded, while Archimedean copulas can be applied only if the generator becomes linear beyond some point. As for the application, we study the problem of capital allocation between risks when the sum of losses is bounded.

Keywords: Copula; functions; Sum; of; dependent; random; variables; Reinsurance (search for similar items in EconPapers)
Date: 2011
References: View references in EconPapers View complete reference list from CitEc
Citations Track citations by RSS feed

Downloads: (external link)
http://www.sciencedirect.com/science/article/B6V8N ... e66d70ab2d7c8d1c9f7e
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: http://EconPapers.repec.org/RePEc:eee:insuma:v:48:y:2011:i:1:p:56-63

Access Statistics for this article

Insurance: Mathematics and Economics is edited by R. Kaas, H. U. Gerber, M. J. Goovaerts and E. S. W. Shiu

More articles in Insurance: Mathematics and Economics from Elsevier
Series data maintained by Wendy Shamier ().