Bayesian modeling of life risk and its applications to securitization

过去半个世纪以来，世界各地的死亡率持续下降。这种下降在老年人中尤其显着，并导致了所谓的长寿风险。近年来，人们对证券化作为对冲系统性风险的一种方式越来越感兴趣。我们在 Lee-Carter 方法论的框架下提出了一种贝叶斯定价长寿风险的方法。具体而言，我们提出了一种贝叶斯方法对幸存者债券进行定价，并设计了相关的幸存者互换。我们的方法基于使用熵最大化原理对未来生存率的预测分布进行风险中和。通过将其应用于日本死亡率来说明该方法。

Over the last half century mortality has declined continuously around the world. The decline has been particularly dramatic in older ages and has caused what is known as longevity risk. In recent years、interest has grown in securitization as a way of hedging the systematic risk. We present a Bayesian approach to pricing longevity risk under the framework of the Lee-Carter methodology. Specifically、we propose a Bayesian method for pricing the survivor bond and the related survivor swap designed. Our method is based on the risk-neutralization of the predictive distribution of future survival rates using the entropy maximization principle. The method is illustrated by applying it to Japanese mortality rates.