Optimal Benefit Distribution of a Tontine-like Annuity Fund with Age-Structured Models
This paper introduces a tontine-like annuity fund designed to provide lifelong income to its participants. Initially, each member contributes a lump-sum payment into a trust fund as a joining premium. Participants then receive benefits over time, based on their survival. As members pass away, their...
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2024-12-01
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| author | Fan Zhang Ping Chen Xueyuan Wu |
| author_facet | Fan Zhang Ping Chen Xueyuan Wu |
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| description | This paper introduces a tontine-like annuity fund designed to provide lifelong income to its participants. Initially, each member contributes a lump-sum payment into a trust fund as a joining premium. Participants then receive benefits over time, based on their survival. As members pass away, their share of payouts is redistributed among the survivors, resulting in increased payouts for those remaining. Differing from traditional tontines, which assume a uniform mortality risk, this fund accommodates participants of various ages and allows new members to join during its operation. To accommodate these features, the authors utilize age-structured models (ASMs) to determine fair premiums for new entrants and to analyze the dynamics of benefit distribution. The core objective of this paper is to develop a pension model using ASMs, recognizing its significant potential for adaptation and expansion. The primary mathematical approach employed is the Maximum Principle from optimal control theory, which helps in deriving explicit solutions for the optimal subsidy strategy. Through numerical examples and detailed illustrations, the paper demonstrates that participants who remain in the cohort longer receive greater subsidies. Additionally, the study finds that adverse shocks lead to a smaller population and thus fewer subsidies. Conversely, starting with a larger initial cohort population tends to increase the overall population, resulting in more subsidies. However, higher costs associated with subsidies lead to their reduction. Our analysis reveals the complex interplay of factors influencing the sustainability and effectiveness of the proposed annuity model. |
| format | Article |
| id | doaj-art-2577186fd18842719794e74452c47ce5 |
| institution | Kabale University |
| issn | 2227-9091 |
| language | English |
| publishDate | 2024-12-01 |
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| spelling | doaj-art-2577186fd18842719794e74452c47ce52025-01-24T13:48:18ZengMDPI AGRisks2227-90912024-12-01131410.3390/risks13010004Optimal Benefit Distribution of a Tontine-like Annuity Fund with Age-Structured ModelsFan Zhang0Ping Chen1Xueyuan Wu2Department of Economics, The University of Melbourne, Parkville, VIC 3010, AustraliaDepartment of Economics, The University of Melbourne, Parkville, VIC 3010, AustraliaDepartment of Economics, The University of Melbourne, Parkville, VIC 3010, AustraliaThis paper introduces a tontine-like annuity fund designed to provide lifelong income to its participants. Initially, each member contributes a lump-sum payment into a trust fund as a joining premium. Participants then receive benefits over time, based on their survival. As members pass away, their share of payouts is redistributed among the survivors, resulting in increased payouts for those remaining. Differing from traditional tontines, which assume a uniform mortality risk, this fund accommodates participants of various ages and allows new members to join during its operation. To accommodate these features, the authors utilize age-structured models (ASMs) to determine fair premiums for new entrants and to analyze the dynamics of benefit distribution. The core objective of this paper is to develop a pension model using ASMs, recognizing its significant potential for adaptation and expansion. The primary mathematical approach employed is the Maximum Principle from optimal control theory, which helps in deriving explicit solutions for the optimal subsidy strategy. Through numerical examples and detailed illustrations, the paper demonstrates that participants who remain in the cohort longer receive greater subsidies. Additionally, the study finds that adverse shocks lead to a smaller population and thus fewer subsidies. Conversely, starting with a larger initial cohort population tends to increase the overall population, resulting in more subsidies. However, higher costs associated with subsidies lead to their reduction. Our analysis reveals the complex interplay of factors influencing the sustainability and effectiveness of the proposed annuity model.https://www.mdpi.com/2227-9091/13/1/4age-structured modelstontinebenefit distributionmaximum principle |
| spellingShingle | Fan Zhang Ping Chen Xueyuan Wu Optimal Benefit Distribution of a Tontine-like Annuity Fund with Age-Structured Models Risks age-structured models tontine benefit distribution maximum principle |
| title | Optimal Benefit Distribution of a Tontine-like Annuity Fund with Age-Structured Models |
| title_full | Optimal Benefit Distribution of a Tontine-like Annuity Fund with Age-Structured Models |
| title_fullStr | Optimal Benefit Distribution of a Tontine-like Annuity Fund with Age-Structured Models |
| title_full_unstemmed | Optimal Benefit Distribution of a Tontine-like Annuity Fund with Age-Structured Models |
| title_short | Optimal Benefit Distribution of a Tontine-like Annuity Fund with Age-Structured Models |
| title_sort | optimal benefit distribution of a tontine like annuity fund with age structured models |
| topic | age-structured models tontine benefit distribution maximum principle |
| url | https://www.mdpi.com/2227-9091/13/1/4 |
| work_keys_str_mv | AT fanzhang optimalbenefitdistributionofatontinelikeannuityfundwithagestructuredmodels AT pingchen optimalbenefitdistributionofatontinelikeannuityfundwithagestructuredmodels AT xueyuanwu optimalbenefitdistributionofatontinelikeannuityfundwithagestructuredmodels |