本篇論文主要討論在死亡率改善不確定性之下的避險策略。當保險公司負債面的人壽保單是比年金商品來得多的時候，公司會處於死亡率的風險之下。我們假設死亡率和利率都是隨機的情況，部分的死亡率風險可以經由自然避險而消除，而剩下的死亡率風險和利率風險則由零息債券和保單貼現商品來達到最適避險效果。我們考慮mean variance、VaR和CTE當成目標函數時的避險策略，其中在mean variance的最適避險策略可以導出公式解。由數值結果我們可以得知保單貼現的確是死亡率風險的有效避險工具。

This paper proposes hedging strategies to deal with the uncertainty of mortality improvement. When insurance company has more life insurance contracts than annuities in the liability, it will be under the exposure of mortality risk. We assume both mortality and interest rate risk are stochastic. Part of mortality risk is eliminated by natural hedging and the remaining mortality risk and interest rate risk will be optimally hedged by zero coupon bond and life settlement contract. We consider the hedging strategies with objective functions of mean variance, value at risk and conditional tail expectation. The closed-form optimal hedging formula for mean variance assumption is derived, and the numerical result show the life settlement is indeed a effective hedging instrument against mortality risk.

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