# Hedging longevity risk in defined contribution pension schemes

## TL;DR

This paper develops an optimal investment framework for pension schemes to hedge longevity risk using mortality-linked securities, demonstrating their effectiveness through mathematical modeling and numerical analysis.

## Contribution

It introduces a novel approach to hedge longevity risk in pension schemes by transforming the problem into an unconstrained optimization and analyzing the impact of mortality-linked securities.

## Key findings

- Longevity risk significantly affects investment strategy performance.
- Mortality-linked securities effectively hedge longevity risk.
- Numerical results support the use of longevity bonds in pension schemes.

## Abstract

Pension schemes all over the world are under increasing pressure to efficiently hedge the longevity risk posed by ageing populations. In this work, we study an optimal investment problem for a defined contribution pension scheme which decides to hedge the longevity risk using a mortality-linked security, typically a longevity bond. The pension scheme invests in the risky assets available in the market, including the longevity bond, by using the contributions from a representative scheme member to ensure a minimum guarantee such that the member is able to purchase a lifetime annuity upon retirement. We transform this constrained optimal investment problem into an unconstrained problem by replicating a self-financing portfolio of future contributions from the member and the minimum guarantee provided by the scheme. We solve the resulting optimisation problem using the dynamic programming principle and through a series of numerical studies reveal that the longevity risk has an important impact on the performance of investment strategies. Our results provide mathematical evidence supporting the use of mortality-linked securities for efficient hedging of the longevity risk.