Bounds and Approximations for sums of dependent log-elliptical random variables

Emil Valdez, Jan Dhaene, Mateusz Maj, Steven Vanduffel

Research output: Contribution to journalArticle

25 Citations (Scopus)

Abstract

Dhaene, Denuit, Goovaerts, Kaas & Vyncke (2002a,b) have studied convex bounds for a sum of dependent random variables and applied these to sums of log-normal random variables. In particular, they have shown how these convex bounds can be used to derive closed-form approximations for several of the risk measures of such a sum. In this paper we investigate to which extent their general results on convex bounds can also be applied to sums of log-elliptical random variables which incorporate sums of log-normals as a special case. Firstly, we show that unlike the log-normal case, for general sums of log-ellipticals the convex lower bound does no longer result in closed form approximations for the different risk measures. Secondly, we demonstrate how instead the weaker stop-loss order can be used to derive such closed form approximations. We also present numerical examples to show the accuracy of the proposed approximations.
Original languageEnglish
Pages (from-to)385-397
Number of pages13
JournalInsurance. Mathematics & Economics
Volume44
Publication statusPublished - Jun 2009

Keywords

  • comonotonicity
  • bounds
  • elliptical distributions
  • log-elliptical distributions

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