CMPH: a multivariate phase-type aggregate loss distribution

Dependence Modeling (2017)

• Volume: 5, Issue: 1, page 304-315
• ISSN: 2300-2298

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Abstract

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We 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.

How to cite

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Jiandong Ren, and Ricardas Zitikis. "CMPH: a multivariate phase-type aggregate loss distribution." Dependence Modeling 5.1 (2017): 304-315. <http://eudml.org/doc/288282>.

@article{JiandongRen2017,
abstract = {We 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.},
author = {Jiandong Ren, Ricardas Zitikis},
journal = {Dependence Modeling},
keywords = {multivariate distribution; compound distribution; Markov chain; risk measure; risk allocation},
language = {eng},
number = {1},
pages = {304-315},
title = {CMPH: a multivariate phase-type aggregate loss distribution},
url = {http://eudml.org/doc/288282},
volume = {5},
year = {2017},
}

TY - JOUR
AU - Jiandong Ren
AU - Ricardas Zitikis
TI - CMPH: a multivariate phase-type aggregate loss distribution
JO - Dependence Modeling
PY - 2017
VL - 5
IS - 1
SP - 304
EP - 315
AB - We 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.
LA - eng
KW - multivariate distribution; compound distribution; Markov chain; risk measure; risk allocation
UR - http://eudml.org/doc/288282
ER -

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