英文标题：
《Optimal Retirement Tontines for the 21st Century: With Reference to
Mortality Derivatives in 1693》
---
作者：
Moshe A. Milevsky, Thomas S. Salisbury
---
最新提交年份：
2013
---
英文摘要：
Historical tontines promised enormous rewards to the last survivors at the expense of those who died early. While this design appealed to the gambling instinct, it is a suboptimal way to manage longevity risk during retirement. This is why fair life annuities making constant payments -- where the insurance company is exposed to the longevity risk -- induces greater lifetime utility. However, tontines do not have to be designed using a winner-take-all approach and insurance companies do not actually sell fair life annuities, partially due to aggregate longevity risk. In this paper we derive the tontine structure that maximizes lifetime utility, but doesn\'t expose the sponsor to any longevity risk. We examine its sensitivity to the size of the tontine pool; individual longevity risk aversion; and subjective health status. The optimal tontine varies with the individual\'s longevity risk aversion $\\gamma$ and the number of participants $n$, which is problematic for product design. That said, we introduce a structure called a natural tontine whose payout declines in exact proportion to the (expected) survival probabilities, which is near-optimal for all $\\gamma$ and $n$. We compare the utility of optimal tontines to the utility of loaded life annuities under reasonable demographic and economic conditions and find that the life annuity\'s advantage over tontines, is minimal. We also review and analyze the first-ever mortality-derivative issued by the British government, known as King Williams\'s tontine of 1693. We shed light on the preferences and beliefs of those who invested in the tontines vs. the annuities and argue that tontines should be re-introduced and allowed to co-exist with life annuities. Individuals would likely select a portfolio of tontines and annuities that suit their personal preferences for consumption and longevity risk, as they did over 320 years ago.
---
中文摘要：
历史上的tontines承诺以牺牲早逝者为代价，向最后的幸存者提供巨额奖励。虽然这种设计迎合了赌博的本能，但它是管理退休期间长寿风险的次优方法。这就是为什么在保险公司面临长寿风险的情况下，持续支付的公平人寿年金会产生更大的终身效用。然而，tontines不必采用赢家通吃的方法进行设计，保险公司也不实际销售公平人寿年金，部分原因是总的长寿风险。在本文中，我们推导出了最大化寿命效用的tontine结构，但不会使赞助者面临任何寿命风险。我们检查了它对tontine池大小的敏感性；个人长寿风险厌恶；以及主观健康状况。最佳tontine因个人的长寿风险厌恶$\\gamma$和参与者人数$\\n$而不同，这对产品设计来说是个问题。这就是说，我们引入了一种称为自然tontine的结构，其支付与（预期）生存概率成正比例下降，这对于所有$\\gamma$和$n$都是接近最优的。在合理的人口和经济条件下，我们比较了最优托尼汀的效用和有载终身年金的效用，发现终身年金相对于托尼汀的优势极校我们还回顾和分析了英国政府发布的第一个死亡率衍生工具，即1693年的威廉姆斯国王托叮我们阐明了投资tontines和年金的人的偏好和信念，并认为tontines应该重新引入，并允许与终身年金共存。个人很可能会像320多年前那样，选择一个适合个人消费偏好和长寿风险的托尼蒂和年金投资组合。
---
分类信息：

一级分类：Quantitative Finance 数量金融学
二级分类：Portfolio Management 项目组合管理
分类描述：Security selection and optimization, capital allocation, investment strategies and performance measurement
证券选择与优化、资本配置、投资策略与绩效评价
--
一级分类：Quantitative Finance 数量金融学
二级分类：General Finance 一般财务
分类描述：Development of general quantitative methodologies with applications in finance
通用定量方法的发展及其在金融中的应用
--

---
PDF下载：
-->