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Copula representations for the sum of dependent risks: models andcomparisons

Abstract: The study of the distributions of sums of dependent risks is a key topic in actuarial sciences, risk management, reliability and in many branches of applied and theoretical probability. However, there are few results where the distribution of the sum of dependent random variables is available in a closed form. In this paper, we obtain several analytical expressions for the distribution of the aggregated risks under dependence in terms of copulas. We provide several representations based on the underlying copula and the marginal distribution functions under general hypotheses and in any dimension. Then, we study stochastic comparisons between sums of dependent risks. Finally, we illustrate our theoretical results by studying some specific models obtained from Clayton, Ali-Mikhail-Haq and Farlie-Gumbel-Morgenstern copulas. Extensions to more general copulas are also included. Bounds and the limiting behavior of the hazard rate function for the aggregated distribution of some copulas are studied as well.

 Fuente: Probability in the Engineering and Informational Sciences, vol. 36, Issue 2, Pages 320 - 340

 Editorial: Cambridge University Press

 Fecha de publicación: 01/04/2022

 Nº de páginas: 20

 Tipo de publicación: Artículo de Revista

 DOI: 10.1017/S0269964820000649

 ISSN: 0269-9648,1469-8951