Bivariate Bernoulli Weighted Sums and Distribution of Single-Period Tontine Benefits

  • Michel Denuit
  • Raluca Vernic


This paper studies the distribution of particular weighted sums of Bernoulli random variables. The computing methods are applied to derive the probability distribution of the random amount of survivor credits to be shared among surviving participants in single-period tontine schemes. The effectiveness of this new arrangement can then be evaluated beyond the classical analysis based on crude approximations for the two first moments, only.


Bernoulli indicator Pure endowment Life tables Individual model Longevity risk 

Mathematics Subject Classification (2010)

62P05 65C20 65C50 


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The authors are very grateful for the helpful comments and the positive opinion expressed by the referee and associate editor about the paper.


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© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Institut de Statistique, Biostatistique et Sciences ActuariellesUniversité Catholique de LouvainLouvain-la-NeuveBelgium
  2. 2.Faculty of Mathematics and InformaticsOvidius University of ConstantaConstantaRomania
  3. 3.Institute for Mathematical Statistics and Applied MathematicsBucharestRomania

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