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

Author

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  • Michel Denuit

    (Université Catholique de Louvain)

  • Raluca Vernic

    (Ovidius University of Constanta
    Institute for Mathematical Statistics and Applied Mathematics)

Abstract

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.

Suggested Citation

  • Michel Denuit & Raluca Vernic, 2018. "Bivariate Bernoulli Weighted Sums and Distribution of Single-Period Tontine Benefits," Methodology and Computing in Applied Probability, Springer, vol. 20(4), pages 1403-1416, December.
    • Handle: RePEc:spr:metcap:v:20:y:2018:i:4:d:10.1007_s11009-018-9625-4
    DOI: 10.1007/s11009-018-9625-4
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    References listed on IDEAS

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    1. Donnelly, C. & Young, J., 2017. "Product options for enhanced retirement income," British Actuarial Journal, Cambridge University Press, vol. 22(3), pages 636-656, September.
    2. Milevsky, Moshe A. & Salisbury, Thomas S., 2016. "Equitable Retirement Income Tontines: Mixing Cohorts Without Discriminating," ASTIN Bulletin, Cambridge University Press, vol. 46(3), pages 571-604, September.
    3. H. Panjer, Harry & Shaun Wang,, 1993. "On the Stability of Recursive Formulas," ASTIN Bulletin, Cambridge University Press, vol. 23(2), pages 227-258, November.
    4. Dhaene, Jan & Vandebroek, Martina, 1995. "Recursions for the individual model," Insurance: Mathematics and Economics, Elsevier, vol. 16(1), pages 31-38, April.
    5. Donnelly, Catherine & Guillén, Montserrat & Nielsen, Jens Perch, 2014. "Bringing cost transparency to the life annuity market," Insurance: Mathematics and Economics, Elsevier, vol. 56(C), pages 14-27.
    6. Stamos, Michael Z., 2008. "Optimal consumption and portfolio choice for pooled annuity funds," Insurance: Mathematics and Economics, Elsevier, vol. 43(1), pages 56-68, August.
    7. Waldmann, Karl-Heinz, 1994. "On the Exact Calculation of the Aggregate Claims Distribution in the Individual Life Model," ASTIN Bulletin, Cambridge University Press, vol. 24(1), pages 89-96, May.
    8. De Pril, Nelson, 1989. "The Aggregate Claims Distribution in the Individual Model with Arbitrary Positive Claims," ASTIN Bulletin, Cambridge University Press, vol. 19(1), pages 9-24, April.
    9. Donnelly, Catherine, 2015. "Actuarial Fairness And Solidarity In Pooled Annuity Funds," ASTIN Bulletin, Cambridge University Press, vol. 45(1), pages 49-74, January.
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    Cited by:

    1. Peter A. Forsyth & Kenneth R. Vetzal & G. Westmacott, 2022. "Optimal performance of a tontine overlay subject to withdrawal constraints," Papers 2211.10509, arXiv.org.
    2. Xie, Lin & Chen, Lv & Qian, Linyi & Li, Danping & Yang, Zhixin, 2023. "Optimal investment and consumption strategies for pooled annuity with partial information," Insurance: Mathematics and Economics, Elsevier, vol. 108(C), pages 129-155.
    3. Moshe A. Milevsky & Thomas S. Salisbury, 2024. "The Riccati Tontine: How to Satisfy Regulators on Average," Papers 2402.14555, arXiv.org.

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