Risk aggregation with FGM copulas

Christopher Blier-Wong, Hélène Cossette and Etienne Marceau

Insurance: Mathematics and Economics, 2023, vol. 111, issue C, 102-120

Abstract: We offer a new perspective on risk aggregation with FGM copulas. Along the way, we discover new results and revisit existing ones, providing simpler formulas than one can find in the existing literature. This paper builds on two novel representations of FGM copulas based on symmetric multivariate Bernoulli distributions and order statistics. First, we detail families of multivariate distributions with closed-form solutions for the cumulative distribution function or moments of the aggregate random variables. We provide methods to compute the cumulative distribution function of aggregate rvs when the marginals are discrete, then order aggregate random variables under the convex order. Finally, we discuss risk-sharing and capital allocation, providing numerical examples for each.

Keywords: Stochastic representation; Mixed Erlang distributions; Stochastic order; Order statistics; Risk-sharing; Capital allocation (search for similar items in EconPapers)
JEL-codes: C02 C46 D81 G22 (search for similar items in EconPapers)
Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:eee:insuma:v:111:y:2023:i:c:p:102-120

DOI: 10.1016/j.insmatheco.2023.03.002

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