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Risk aggregation with FGM copulas

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  • Blier-Wong, Christopher
  • Cossette, Hélène
  • Marceau, Etienne

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.

Suggested Citation

  • Blier-Wong, Christopher & Cossette, Hélène & Marceau, Etienne, 2023. "Risk aggregation with FGM copulas," Insurance: Mathematics and Economics, Elsevier, vol. 111(C), pages 102-120.
    • Handle: RePEc:eee:insuma:v:111:y:2023:i:c:p:102-120
    DOI: 10.1016/j.insmatheco.2023.03.002
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    More about this item

    Keywords

    Stochastic representation; Mixed Erlang distributions; Stochastic order; Order statistics; Risk-sharing; Capital allocation;
    All these keywords.

    JEL classification:

    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
    • C46 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Specific Distributions
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies

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