# CMPH: a multivariate phase-type aggregate loss distribution

CMPH: a multivariate phase-type aggregate loss distribution AbstractWe introduce a compound multivariate distribution designed for modeling insurance losses arising from different risk sources in insurance companies. The distribution is based on a discrete-time Markov Chain and generalizes the multivariate compound negative binomial distribution, which is widely used for modeling insurance losses.We derive fundamental properties of the distribution and discuss computational aspects facilitating calculations of risk measures of the aggregate loss, as well as allocations of the aggregate loss to individual types of risk sources. Explicit formulas for the joint moment generating function and the joint moments of different loss types are derived, and recursive formulas for calculating the joint distributions given. Several special cases of particular interest are analyzed. An illustrative numerical example is provided. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Dependence Modeling de Gruyter

# CMPH: a multivariate phase-type aggregate loss distribution

Dependence Modeling, Volume 5 (1): 12 – Dec 20, 2017
12 pages

/lp/degruyter/cmph-a-multivariate-phase-type-aggregate-loss-distribution-LkVayvxe4H
Publisher
de Gruyter
ISSN
2300-2298
eISSN
2300-2298
D.O.I.
10.1515/demo-2017-0018
Publisher site
See Article on Publisher Site

### Abstract

AbstractWe introduce a compound multivariate distribution designed for modeling insurance losses arising from different risk sources in insurance companies. The distribution is based on a discrete-time Markov Chain and generalizes the multivariate compound negative binomial distribution, which is widely used for modeling insurance losses.We derive fundamental properties of the distribution and discuss computational aspects facilitating calculations of risk measures of the aggregate loss, as well as allocations of the aggregate loss to individual types of risk sources. Explicit formulas for the joint moment generating function and the joint moments of different loss types are derived, and recursive formulas for calculating the joint distributions given. Several special cases of particular interest are analyzed. An illustrative numerical example is provided.

### Journal

Dependence Modelingde Gruyter

Published: Dec 20, 2017

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