A note on bequest preferences in utility maximisation for modern tontines
这篇短文探讨了现代唐提式养老金中遗赠偏好与效用最大化问题，提出了验证最优控制和资金分配递减的方法，并指出遗赠偏好应随时间变化以避免不切实际的投资策略。
In this short note, we address two issues in the literature about modern tontines with bequest and utility maximisation: how to verify optimal controls and the decreasing allocation of funds in the tontine. We want to raise awareness about the dual approach to solve optimal control problems when working with power utilities in the actuarial community. Additionally, we highlight that bequest preferences should be time-dependent or otherwise yield unrealistic investment strategies. We base our attempt at modelling bequest preferences on rules like 100% payback upon death at the start that vanishes over time. Our modelling shows that the resulting investment strategy almost linearly adjusts the allocation in the tontine from 0% to 100% over time.