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Multivariate distribution defined with Farlie-Gumbel-Morgenstern copula and mixed Erlang marginals: aggregation and capital allocation. (English) Zbl 1284.60027

Summary: 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.

MSC:

60E05 Probability distributions: general theory
62H05 Characterization and structure theory for multivariate probability distributions; copulas
62E15 Exact distribution theory in statistics
91B30 Risk theory, insurance (MSC2010)
91G10 Portfolio theory
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