Third Cumulant for Multivariate Aggregate Claim Models
(2015) In Working Papers in Statistics- Abstract
- 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... (More)
- 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. (Less)
Please use this url to cite or link to this publication:
http://lup.lub.lu.se/record/8310038
- author
- Loperfido, Nicola; Mazur, Stepan ^{LU} and Podgorski, Krzysztof ^{LU}
- organization
- publishing date
- 2015
- type
- Working Paper
- publication status
- published
- subject
- keywords
- Third cumulant, multivariate aggregate claim, skew-normal, Laplace motion
- in
- Working Papers in Statistics
- issue
- 13
- pages
- 30 pages
- publisher
- Department of Statistics, Lund university
- language
- English
- LU publication?
- yes
- id
- 2eb47fca-f6d5-45cd-bdb5-af331591ce6c (old id 8310038)
- date added to LUP
- 2015-12-09 16:36:51
- date last changed
- 2016-04-16 10:03:20
@misc{2eb47fca-f6d5-45cd-bdb5-af331591ce6c, abstract = {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.}, author = {Loperfido, Nicola and Mazur, Stepan and Podgorski, Krzysztof}, keyword = {Third cumulant,multivariate aggregate claim,skew-normal,Laplace motion}, language = {eng}, number = {13}, pages = {30}, publisher = {ARRAY(0x9581680)}, series = {Working Papers in Statistics}, title = {Third Cumulant for Multivariate Aggregate Claim Models}, year = {2015}, }