Multivariate distribution defined with Farlie–Gumbel–Morgenstern copula and mixed Erlang marginals: Aggregation and capital allocation

Hélène Cossette, Marie-Pier Côté, Etienne Marceau and Khouzeima Moutanabbir

Insurance: Mathematics and Economics, 2013, vol. 52, issue 3, 560-572

Abstract: In this paper, we investigate risk aggregation and capital allocation problems for a portfolio of possibly dependent risks whose multivariate distribution is defined with the Farlie–Gumbel–Morgenstern copula and mixed Erlang distribution marginals. In such a context, we first show that the aggregate claim amount has a mixed Erlang distribution. Based on a top-down approach, closed-form expressions for the contribution of each risk are derived using the TVaR and covariance rules. These findings are illustrated with numerical examples.

Keywords: Aggregate claim loss; Risk measures; Capital allocation; Tail-Value-at-Risk; FGM copula; TVaR-based allocation rule; Covariance-based allocation rule; Mixed Erlang distribution (search for similar items in EconPapers)
Date: 2013
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Citations: View citations in EconPapers (22)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:insuma:v:52:y:2013:i:3:p:560-572

DOI: 10.1016/j.insmatheco.2013.03.006

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