Webbläsaren som du använder stöds inte av denna webbplats. Alla versioner av Internet Explorer stöds inte längre, av oss eller Microsoft (läs mer här: * https://www.microsoft.com/en-us/microsoft-365/windows/end-of-ie-support).

Var god och använd en modern webbläsare för att ta del av denna webbplats, som t.ex. nyaste versioner av Edge, Chrome, Firefox eller Safari osv.

Third Cumulant for Multivariate Aggregate Claim Models

In English

Författare

Summary, in English

The third moment 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. It is discussed how this result can be used to obtain a formula for the third cumulant for a classical model of multivariate claims. Two important special cases are considered. In the rst 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.

Publiceringsår

2015

Språk

Engelska

Publikation/Tidskrift/Serie

Working Papers in Statistics

Issue

13

Dokumenttyp

Working paper

Förlag

Department of Statistics, Lund university

Ämne

  • Probability Theory and Statistics

Nyckelord

  • Third cumulant
  • multivariate aggregate claim
  • skew-normal
  • Laplace motion

Status

Published