Longevity risk, i.e. the risk of unexpected changes in the survivorship of policyholders, is perceived as one of the major threats to the long-run solvency of annuity providers, such as pension funds. Continuous-time models represent a useful tool in the modelling of stochastic mortality. Non-mean reverting affine cohort processes (Luciano and Vigna, 2008)provide a parsimonious but accurate description of mortality tables. They are particularly suited to pricing and hedging purposes, due to their analytical tractability. I present applications of such models to the management of insurance portfolios. I focus on longevity risk hedging techniques, such as natural hedging, and reinsurance strategies. I will discuss the implementation and the effectiveness of such strategies, as well as the effects of different risk sources (interest-rate risk, investment risk) - along with longevity risk - on the solvency of insurers.