Optimal hedging of longevity risks for group self-annuity portfolios

Abstract

This paper proposes a dynamic longevity risk hedging strategy for smooth survival benefit profiles of group self-annuity (GSA) schemes in the presence of population basis risk. The fund manager of GSA acts on behalf of fund participants in selecting the optimal hedge. The hedging framework is formulated as a mean-variance optimization problem, which serves as a theoretical framework for selecting the optimal hedging strategy. The hedging mechanism involves trading standardized longevity-linked securities dynamically. A semi-analytic solution to the optimal hedge ratio is derived, which enhances the numerical implementation of the strategy. Furthermore, a risk decomposition method is developed, enabling hedging of various sources of risks, such as longevity and investment risks. Numerical illustrations highlight that the hedging strategy effectively mitigates variability in survival benefits. Meanwhile, a holistic risk management framework utilizing the longevity risk hedging strategy and a target volatility investment strategy increases the fund's return per unit of risk.