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ON SARMANOV MIXED ERLANG RISKS IN INSURANCE APPLICATIONS

Published online by Cambridge University Press:  07 October 2014

Enkelejd Hashorva  and
Gildas Ratovomirija
Enkelejd Hashorva
Affiliation:
Department of Actuarial Science, Faculty of Business and Economics, University of Lausanne, UNIL-Dorigny 1015 Lausanne, Switzerland E-Mail address: Enkelejd.Hashorva@unil.ch
Gildas Ratovomirija*
Affiliation:
Department of Actuarial Science, Faculty of Business and Economics, University of Lausanne, UNIL-Dorigny 1015 Lausanne, Switzerland
*
E-Mail address: Gildas.Ratovomirija@unil.ch, gra@vaudoise.ch
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Abstract

In this paper we consider an extension to the aggregation of the FGM mixed Erlang risks, proposed by Cossette et al. (2013 Insurance: Mathematics and Economics, 52, 560–572), in which we introduce the Sarmanov distribution to model the dependence structure. For our framework, we demonstrate that the aggregated risk belongs to the class of Erlang mixtures. Following results from S. C. K. Lee and X. S. Lin (2010 North American Actuarial Journal, 14(1) 107–130), G. E. Willmot and X. S. Lin (2011 Applied Stochastic Models in Business and Industry, 27(1) 8–22), analytical expressions of the contribution of each individual risk to the economic capital for the entire portfolio are derived under both the TVaR and the covariance capital allocation principle. By analysing the commonly used dependence measures, we also show that the dependence structure is wide and flexible. Numerical examples and simulation studies illustrate the tractability of our approach.

Keywords

Risk aggregationSarmanov distributionmixed Erlang distributiondependence measurescapital allocation
Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 45 , Issue 1 , January 2015 , pp. 175 - 205
Copyright
Copyright © ASTIN Bulletin 2014 

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