EconPapers    
Economics at your fingertips  
 

On a Multiplicative Multivariate Gamma Distribution with Applications in Insurance

Vadim Semenikhine (), Edward Furman () and Jianxi Su ()
Additional contact information
Vadim Semenikhine: Department of Mathematics and Statistics, York University, Toronto, ON M3J 1P3, Canada
Edward Furman: Department of Mathematics and Statistics, York University, Toronto, ON M3J 1P3, Canada
Jianxi Su: Department of Statistics, Purdue University, West Lafayette, IN 47906, USA

Risks, 2018, vol. 6, issue 3, 1-20

Abstract: One way to formulate a multivariate probability distribution with dependent univariate margins distributed gamma is by using the closure under convolutions property. This direction yields an additive background risk model, and it has been very well-studied. An alternative way to accomplish the same task is via an application of the Bernstein–Widder theorem with respect to a shifted inverse Beta probability density function. This way, which leads to an arguably equally popular multiplicative background risk model (MBRM), has been by far less investigated. In this paper, we reintroduce the multiplicative multivariate gamma (MMG) distribution in the most general form, and we explore its various properties thoroughly. Specifically, we study the links to the MBRM, employ the machinery of divided differences to derive the distribution of the aggregate risk random variable explicitly, look into the corresponding copula function and the measures of nonlinear correlation associated with it, and, last but not least, determine the measures of maximal tail dependence. Our main message is that the MMG distribution is (1) very intuitive and easy to communicate, (2) remarkably tractable, and (3) possesses rich dependence and tail dependence characteristics. Hence, the MMG distribution should be given serious considerations when modelling dependent risks.

Keywords: multivariate gamma distribution; multiplicative background risk model; aggregate risk; individual risk model; collective risk model (search for similar items in EconPapers)
JEL-codes: C G0 G1 G2 G3 M2 M4 K2 (search for similar items in EconPapers)
Date: 2018
References: View references in EconPapers View complete reference list from CitEc
Citations Track citations by RSS feed

Downloads: (external link)
https://www.mdpi.com/2227-9091/6/3/79/pdf (application/pdf)
https://www.mdpi.com/2227-9091/6/3/79/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jrisks:v:6:y:2018:i:3:p:79-:d:163347

Access Statistics for this article

Risks is currently edited by Prof. Dr. J. David Cummins

More articles in Risks from MDPI, Open Access Journal
Bibliographic data for series maintained by XML Conversion Team ().

 
Page updated 2018-10-02
Handle: RePEc:gam:jrisks:v:6:y:2018:i:3:p:79-:d:163347