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Fairness and risk sharing in integrated LRD-tontine schemes under Volterra mortality risk

Published online by Cambridge University Press:  31 July 2025

Jingwen Kang ,
Zhuo Jin Open the ORCID record for Zhuo Jin [Opens in a new window] ,
Linyi Qian  and
Nan Zhang Open the ORCID record for Nan Zhang [Opens in a new window]
Jingwen Kang
Affiliation:
Key Laboratory of Advanced Theory and Application in Statistics and Data Science-MOE, School of Statistics East China Normal University Shanghai 200062, China
Zhuo Jin
Affiliation:
Department of Actuarial Studies and Business Analytics, Macquarie University, Sydney, NSW 2109, Australia
Linyi Qian
Affiliation:
Key Laboratory of Advanced Theory and Application in Statistics and Data Science-MOE, School of Statistics, China Inclusive Ageing Finance Research Center, East China Normal University, Shanghai 200062, China
Nan Zhang*
Affiliation:
Key Laboratory of Advanced Theory and Application in Statistics and Data Science-MOE, School of Statistics, China Inclusive Ageing Finance Research Center, East China Normal University, Shanghai 200062, China
*
Corresponding author: Nan Zhang; Email: nzhang@sfs.ecnu.edu.cn
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Abstract

As the global elderly population expands, the associated risks of longevity intensify, presenting significant challenges to traditional retirement security systems. We study actuarial fairness in tontines under the Volterra mortality framework, integrating long-range dependence mortality models rates with tontine structures. Initially, we establish an optimal tontine model for a homogeneous tontine under this framework. However, according only to individual actuarial fairness can neglect the collective nature of tontines. So we propose a hybrid optimization model that accounts for age and wealth discrepancies affecting payment amounts and the collective fairness. Specially, we first apply the f-value fairness measure in age-heterogeneous tontines for assessing fairness. Our results reveal that while the model ensures actuarial fairness at the group level, relative payments are lower for older age groups. By incorporating dynamic mortality modeling through the Volterra mortality framework, our work demonstrates that this comprehensive scheme significantly enhances the robustness and sustainability of retirement security systems. These findings provide valuable insights for the future integration of dynamic mortality models with innovative retirement income structures.

Keywords

TontineActuarial fairnessVolterra processRisk sharingLong range dependence

Information

Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 55 , Special Issue 3: Risk Sharing , September 2025 , pp. 644 - 667
Copyright
© The Author(s), 2025. Published by Cambridge University Press on behalf of The International Actuarial Association

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