Immacolata Oliva - Pension funds with longevity risk: an optimal portfolio insurance approach

This paper investigates an optimal investment problem within a defined contribution (DC) pension scheme, providing minimum guarantee protection and including longevity risk. The representative fund members’ contributions are allocated into a risky asset and a bond following a proportional portfolio insurance strategy, to provide fund members with a life annuity at retirement. More precisely, we employ a strategy whose floor is linked to the actuarial present value of the annuity to be purchased at maturity. The picture is completed by including a stochastic force of mortality
and a stochastic interest rate, following a mean-reverting square-root process and a Vasicek model, respectively. We further assume that the DC pension fund contribution rate is stochastic and correlated with the risk factors mentioned above. We solve the resulting optimization problem using standard dynamic programming techniques and provide a numerical study to measure the impact of longevity risk on the investment strategy’s performance.