Tail index-linked annuity: A longevity risk sharing retirement plan

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.