Krzysztof Podgórski
Professor, Head of the Department of Statistics
Third Cumulant for Multivariate Aggregate Claim Models
Author
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.
Department/s
- Department of Statistics
Publishing year
2015
Language
English
Publication/Series
Working Papers in Statistics
Issue
13
Full text
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Document type
Working paper
Publisher
Department of Statistics, Lund university
Topic
- Probability Theory and Statistics
Keywords
- Third cumulant
- multivariate aggregate claim
- skew-normal
- Laplace motion
Status
Published