Variable annuities are products offered by pension funds and life offices that provide periodic future payments to the investor and often have ancillary benefits that guarantee survival benefits or sums insured on death. This paper extends the benchmark approach to value and hedge long-dated variable annuities using a combination of cash, bonds and equities under a variety of market models, allowing for dependence between financial and insurance markets. Under a simplified case of independence, the results show that when the discounted index is modelled as a time-transformed squared Bessel process, less-expensive valuation and reserving is achieved regardless of the short rate model or the mortality model.

中文翻译：

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当利率和死亡率是随机的时，对长期可变年金的价格偏低的估值和保留

可变年金是养老基金和人寿办事处提供的产品，可定期向投资者提供未来付款，并经常具有辅助利​​益，以保证生存利益或死亡时的保额。本文将在各种市场模型下使用现金，债券和股票的组合将基准方法扩展到价值和对冲长期可变年金，从而允许金融和保险市场之间的依赖。在简化的独立性情况下，结果表明，将折现指数建模为时间转换的平方贝塞尔过程时，无论短期利率模型还是死亡率模型，都可以实现较便宜的估值和保留。