This paper proposes an innovative retirement product focusing on longevity risk sharing, a contract we refer to as tail index-linked annuity (TILA). Specifically, the proposed TILA pays out variable annual payments, which will be equal to a regular nominal amount when a reference survival index is lower than a predetermined threshold (i.e. normal evolution of longevity risk), and a reduced, index-dependent payment when the threshold is passed (i.e. highly unfavorable evolution of longevity risk). The proposed TILA aims at not only improving the benefits of the policyholders, which has been the focus in recent literature on innovative retirement products, but also reducing the longevity risk exposure of the insurer, particularly for advanced retirement ages. Using real-world mortality data and a stochastic multi-population mortality model, we find that the proposed TILA leads to higher expected lifetime utility than regular annuities for policyholders with different degrees of risk aversions. Meanwhile, numerical analysis shows that the proposed TILA could greatly mitigate the solvency risk of the insurer, leading to a substantially lower loss probability and expected (tail-) loss than regular annuities in the presence of a longevity shock, and therefore could reduce the insurer's required solvency capital under the latest solvency regulations.

本文提出了一种专注于长寿风险分担的创新型退休产品，我们将其称为尾指数挂钩年金（TILA）。具体而言，提议的 TILA 支付可变的年度付款，当参考生存指数低于预定阈值（即长寿风险的正常演变）时，这将等于常规名义金额，当阈值已通过（即长寿风险的高度不利演变）。拟议的 TILA 不仅旨在提高投保人的福利（这一直是近期文献中关于创新退休产品的重点），而且还旨在降低保险公司的长寿风险敞口，特别是对于高龄退休人员。使用真实世界的死亡率数据和随机多人口死亡率模型，我们发现，对于风险厌恶程度不同的投保人来说，提议的 TILA 比普通年金具有更高的预期终生效用。同时，数值分析表明，提议的 TILA 可以大大降低保险公司的偿付能力风险，导致在存在长寿冲击的情况下，与普通年金相比，损失概率和预期（尾部）损失大大降低，因此可以降低保险公司的偿付能力风险。最新偿付能力规定要求的偿付能力资本。