  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.
