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On the moments of aggregate discounted claims with dependence introduced by a FGM copula. (English) Zbl 1214.91050

Summary: We investigate the computation of the moments of the compound Poisson sums with discounted claims when introducing dependence between the interclaim time and the subsequent claim size. The dependence structure between the two random variables is defined by a Farlie-Gumbel-Morgenstern copula. Assuming that the claim distribution has finite moments, we give expressions for the first and the second moments and then we obtain a general formula for any \(m\)th order moment. The results are illustrated with applications to premium calculation and approximations based on moment matching methods.

MSC:

91B30 Risk theory, insurance (MSC2010)
62P05 Applications of statistics to actuarial sciences and financial mathematics
62H20 Measures of association (correlation, canonical correlation, etc.)
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