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ON SOME PROPERTIES OF A CLASS OF MULTIVARIATE ERLANG MIXTURES WITH INSURANCE APPLICATIONS

Published online by Cambridge University Press:  23 September 2014

Gordon E. Willmot  and
Jae-Kyung Woo
Gordon E. Willmot
Affiliation:
Department of Statistics and Actuarial Science, University of Waterloo, 200 University Avenue West, Waterloo, Canada E-mail: [email protected]
Jae-Kyung Woo*
Affiliation:
Department of Statistics and Actuarial Science, University of Hong Kong, Pokfulam Road, Hong Kong
*
E-mail: [email protected]
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Abstract

We discuss some properties of a class of multivariate mixed Erlang distributions with different scale parameters and describes various distributional properties related to applications in insurance risk theory. Some representations involving scale mixtures, generalized Esscher transformations, higher-order equilibrium distributions, and residual lifetime distributions are derived. These results allows for the study of stop-loss moments, premium calculation, and the risk allocation problem. Finally, some results concerning minimum and maximum variables are derived and applied to pricing joint life and last survivor policies.

Keywords

Multivariate mixed Erlangscale mixturesgeneralized Esscher transformationstop-loss momentsresidual lifetime distributionrisk measurescapital allocationjoint and last survivor
Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 45 , Issue 1 , January 2015 , pp. 151 - 173
Copyright
Copyright © ASTIN Bulletin 2014 

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