具有遗赠动机的显式现代理想汤图的封闭解
Closed-form Solutions for an Explicit Modern Ideal Tontine with Bequest Motive
摘要：
在本文中，我扩展了Bernhardt和Donnelly（2019）关于现代显性养老金的研究，作为一种在特定遗赠动机下从固定缴款养老金罐中提供收入的方式。本文件的一个主要特点是，它放宽了投资于养老金和遗赠账户的固定比例的假设。在使遗赠比例的一个额外的控制功能，我得到了迄今为止，封闭形式的解决方案的部分消费率，财富，遗赠金额，遗赠比例下一个恒定的相对风险厌恶效用。我表明，最佳遗赠比例是产品的最佳分数消费率和一个指数遗赠参数。我表明，在某些情况下，如一个非常高的遗赠动机，一个生命周期的效用最大化战略将需要负死亡率信贷类似于一个成员支付人寿保险费。典型的情况下，探讨使用英国国家统计局的生命表。
英文摘要：
In this paper I extend the work of Bernhardt and Donnelly (2019) dealing with modern explicit tontines, as a way of providing income under a specified bequest motive, from a defined contribution pension pot. A key feature of the present paper is that it relaxes the assumption of fixed proportions invested in tontine and bequest accounts. In making the bequest proportion an additional control function I obtain, hitherto unavailable, closed-form solutions for the fractional consumption rate, wealth, bequest amount, and bequest proportion under a constant relative risk averse utility. I show that the optimal bequest proportion is the product of the optimum fractional consumption rate and an exponentiated bequest parameter. I show that under certain circumstances, such as a very high bequest motive, a life-cycle utility maximisation strategy will necessitate negative mortality credits analogous to a member paying life insurance premiums. Typical scenarios are explored using UK Office of National Statistics life tables.
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