Life expectancy in most parts of the world has increased substantially in the past few decades. For example, the life expectancy at birth for a Dutch male increased from 70.3 years in 1950 to 79.9 in 2014, while this number for a Dutch female increased from 72.6 years in 1950 to 83.3 years in 2014.1 Formally, we refer to longevity risk as the risk due to unexpected changes of the mortality rates of populations. During recent years, longevity risk has attracted more and more attention from pension plans and annuity providers. In particular, as an innovative way to transfer longevity risk, the longevity-linked capital market is developing rapidly. According to the records on Artemis,2 the volume of transactions in the U.K. longevity-linked capital market has increased from £3.4 billion in year 2009 to £21.9 billion in year 2014. In this thesis we consider the management of longevity risk in the view of pension plans and annuity providers, including the forecast of future mortality rates and the hedging of mortality risk using longevity-linked derivatives.