Third cumulant for multivariate aggregate claim models

Forskningsoutput: TidskriftsbidragArtikel i vetenskaplig tidskrift


The third cumulant for the aggregated multivariate claims is considered. A formula is presented for the general case when the aggregating variable is independent of the multivariate claims. Two important special cases are considered. In the first one, multivariate skewed normal claims are considered and aggregated by a Poisson variable. The second case is dealing with multivariate asymmetric generalized Laplace and aggregation is made by a negative binomial variable. Due to the invariance property the latter case can be derived directly, leading to the identity involving the cumulant of the claims and the aggregated claims. There is a well-established relation between asymmetric Laplace motion and negative binomial process that corresponds to the invariance principle of the aggregating claims for the generalized asymmetric Laplace distribution. We explore this relation and provide multivariate continuous time version of the results. It is discussed how these results that deal only with dependence in the claim sizes can be used to obtain a formula for the third cumulant for more complex aggregate models of multivariate claims in which the dependence is also in the aggregating variables.


Enheter & grupper
Externa organisationer
  • University of Urbino
  • Örebro University

Ämnesklassifikation (UKÄ) – OBLIGATORISK

  • Sannolikhetsteori och statistik


Sidor (från-till)109-128
TidskriftScandinavian Actuarial Journal
Utgåva nummer2
Tidigt onlinedatum2017 mar 26
StatusPublished - 2018 feb 7
Peer review utfördJa

Relaterad forskningsoutput

Loperfido, N., Mazur, S. & Krzysztof Podgorski, 2015, Department of Statistics, Lund university, 30 s. (Working Papers in Statistics; nr. 13).

Forskningsoutput: Working paper

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