Tails of the Moments for Sums with Dominatedly Varying Random Summands

Mantas Dirma, Saulius Paukštys and Jonas Šiaulys
Additional contact information
Mantas Dirma: Institute of Mathematics, Vilnius University, Naugarduko 24, LT-03225 Vilnius, Lithuania
Saulius Paukštys: Institute of Mathematics, Vilnius University, Naugarduko 24, LT-03225 Vilnius, Lithuania
Jonas Šiaulys: Institute of Mathematics, Vilnius University, Naugarduko 24, LT-03225 Vilnius, Lithuania

Mathematics, 2021, vol. 9, issue 8, 1-26

Abstract: The asymptotic behaviour of the tail expectation ? E ( S n ξ ) α ? { S n ξ > x } is investigated, where exponent α is a nonnegative real number and S n ξ = ξ 1 + … + ξ n is a sum of dominatedly varying and not necessarily identically distributed random summands, following a specific dependence structure. It turns out that the tail expectation of such a sum can be asymptotically bounded from above and below by the sums of expectations ? E ξ i α ? { ξ i > x } with correcting constants. The obtained results are extended to the case of randomly weighted sums, where collections of random weights and primary random variables are independent. For illustration of the results obtained, some particular examples are given, where dependence between random variables is modelled in copulas framework.

Keywords: tail expectation; asymptotic bound; quasi-asymptotic independence; heavy-tailed distribution; dominated variation; copula (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (3)

Downloads: (external link)
https://www.mdpi.com/2227-7390/9/8/824/pdf (application/pdf)
https://www.mdpi.com/2227-7390/9/8/824/ (text/html)

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: https://EconPapers.repec.org/RePEc:gam:jmathe:v:9:y:2021:i:8:p:824-:d:533481

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().