<abstract><p>Longevity risk is the risk that members of a given population will live longer than expected. When it occurs, pension providers may have to pay pensions for longer than expected, significantly increasing their costs. While this risk is being adequately studied using the national mortality data provided by the Human Mortality Database, relatively few studies exist that analyse sub-national data. This manuscript proposes a comparative study of some stochastic mortality models to measure the longevity risk on Italian mortality data at the regional level. In particular, the use of the Lee-Carter and Li-Lee models is explored. The models are compared in fitting quality, forecasting accuracy and complexity. Numerical experiments and applications to immediate life annuity evaluation are presented.</p></abstract>

中文翻译：

---

长寿风险分析：意大利地区数据的应用

<abstract><p>长寿风险是特定人群中的成员寿命比预期长的风险。当这种情况发生时，养老金提供者可能不得不支付比预期更长的养老金，从而显着增加他们的成本。虽然使用人类死亡率数据库提供的国家死亡率数据对这种风险进行了充分研究，但分析地方数据的研究相对较少。这份手稿提出了一些随机死亡率模型的比较研究，以衡量意大利死亡率数据在区域层面的长寿风险。特别是探索了 Lee-Carter 和 Li-Lee 模型的使用。这些模型在拟合质量、预测准确性和复杂性方面进行了比较。介绍了即时年金评估的数值实验和应用。</p></abstract>