Optimal Control of Continuous Benefit Tontine with Age-Structured Models
This paper studies the optimal control problems of continuous-benefit tontine funds and multicohort tontine models. Firstly, we take a limit on the number of members in the tontine pool and obtain a continuous form of benefits by Borel’s law of large numbers. This continuous framework provides greater flexibility compared to the traditional binomial model for designing future pension products based on tontines. Also, the new framework could disguise tontines as mortality-linked annuities, which might allow the legal provisions of life annuities to be used to circumvent certain bans on tontine products. In contrast to a normal Defined Contribution (DC) pension, tontine policyholders essentially give up their right to inherit the account balances at death in exchange for a higher rate of return. Furthermore, a dynamic equation is derived revealing that the extra return rate is just the instantaneous mortality rate of the policyholder. In the multi-cohort context, this paper employs some age-structured models with shocks to model a tontine, so that the overall benefit of the fund can be optimally controlled. Based on the idea of shares, a concept of shadow account is proposed in this paper, followed by indirect controls on the account, which could shed a light for governments to divert some political pressure on tontine-based pension funds. If an individual wanted to join a tontine fund at a self-selected time, the person has to contribute an amount of money equals the balance of the shadow account of an existing member at the same age at that time. This is a valuable addition to the current literature as little has been done regarding the open-end tontine funds so far. Our numerical simulations show that the optimal control is to subsidise early entrants and younger members by penalising older members. This result makes much sense because early entrants and young members do not enjoy high rates of return as older members, nor do they enjoy the investment returns in the pool. Small deductions in benefits for older members would not downgrade the quality of their life because the benefits have grown to a relatively high level
Year of publication: |
[2023]
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Authors: | Zhang, Fan |
Publisher: |
[S.l.] : SSRN |
Saved in:
freely available
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