CMPH: a multivariate phase-type aggregate loss distribution

• Autorzy: Jiandong Ren , Ricardas Zitikis
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

multivariate distribution; compound distribution; Markov chain; risk measure; risk allocation

Kategorie tematyczne

• 62E10: Characterization and structure theory
• 60J20: Applications of Markov chains and discrete-time Markov processes on general state spaces (social mobility, learning theory, industrial processes, etc.)
• 62P05: Applications to actuarial sciences and financial mathematics
• 60E05: Distributions: general theory

• Wydawca: De Gruyter Open
• Czasopismo: Dependence Modeling
• Rocznik: 2017
• Tom: 5
• Numer: 1
• Strony: 304-315

Daty

wydano

2017-12-20

otrzymano

2017-08-29

zaakceptowano

2017-12-02

online

2017-12-29

Twórcy

autor

Jiandong Ren

• N6A 5B7,

autor

Ricardas Zitikis

• N6A 5B7,

Identyfikatory

DOI

10.1515/demo-2017-0018