Temporal and spatial correlations in mortality dynamics: Applications to mortality/longevity risk management

人们早就认识到死亡率动态的随机性。它在两个维度上影响着金融业。一方面，养恤金和年金的提供者面临长寿风险，因为预期寿命的意外增加将延长支付养恤金/年金的期限。根据国际货币基金组织（imf）的数据，全球长寿风险敞口估计在15至25万亿美元之间。另一方面，寿险公司面临灾难性死亡事件带来的风险，这将导致死亡率过高，从而导致更高的人寿保险赔付。研究发现，类似1957年和1968年爆发的中度流感大流行可能使美国人寿保险公司额外索赔150亿美元。COVID-19大流行对人寿保险赔付的影响尚未估计，但考虑到其规模和全球影响力，影响可能非常大。拟议研究的长期目标是更好地了解死亡率和寿命风险，重点是大量人口死亡率动态之间的相互依赖关系，以及这种相互依赖关系的财政影响。这项研究从大量关于这一广泛主题的现有工作中脱颖而出，因为它关注的是死亡率/寿命暴露之间的全球联系。报告还特别关注最近的死亡率趋势和事件，包括自2010年代中期以来在一些发达国家观察到的预期寿命下降。具体而言，拟议研究的目标有三个：第一个目标是利用先进的高维数据分析技术研究死亡率改善率的空间相关性。通过利用空间相关性，我将识别多元化机会，并制定可能优于现有对冲策略的对冲策略。第二个目标是建立一个能够同时捕捉多个地区灾难性死亡事件的模型。该模型不仅将有助于再保险和死亡率巨灾债券的定价，而且还将改进具有多国死亡率风险敞口的保险公司的风险管理解决方案。第三个目标是开发一种方法，利用先进的时间相关模型捕捉死亡率改善的波动。利用由此产生的模型，我将开发依赖于制度的对冲策略，这将允许更有效地降低长寿风险。加拿大的长寿风险转移市场正在迅速增长。仅在2019年，加拿大再保险公司就完成了四笔数十亿美元的交易。加拿大的金融行业现在需要先进的随机死亡率模型和风险管理方法的知识，这些学生将在拟议的研究中获得。研究成果也将加强加拿大在市场上的地位，因为它们正在被养老金和再保险行业的从业者所采用。

The stochastic nature of mortality dynamics has long been recognized. It affects the financial industry in two dimensions. On one hand, providers of pensions and annuities are subject to longevity risk, as an unexpected increase in life expectancy would lengthen the duration over which pension/annuity payments are made. According to the International Monetary Fund, global longevity risk exposure estimates range from 15 to 25 trillion USD. On the other hand, life insurers are exposed to risks arising from catastrophic mortality events, which would lead to excess mortality and consequently higher life insurance payouts. Research has found that a moderate influenza pandemic similar to the 1957 and 1968 outbreaks could cost US life insurers 15 billion USD in additional claims. The impact of the COVID-19 pandemic on life insurance payouts is yet to be estimated, but it is likely to be very significant given its scale and global presence. The long-term goal of the proposed research is to develop a better understanding of mortality and longevity risks, with a focus on the interdependency among the mortality dynamics of large collections of populations, and the financial implications of such an interdependency. This research stands out from the abundant existing works on this broad theme in its focus on the global connections among mortality/longevity exposures. It is also unique in its attention to recent mortality trends and events, including the decline in life expectancy observed in some developed countries since the mid-2010s. Specifically, the objectives of the proposed research are threefold: The first objective is to study spatial correlations of mortality improvement rates with advanced high-dimensional data analytic techniques. By exploiting spatial correlations, I will identify diversification opportunities and develop hedging strategies that are likely to outperform existing ones. The second objective is to develop a model that captures catastrophic mortality events in multiple regions simultaneously. The model will not only aid pricing reinsurance and mortality catastrophe bonds, but also improve risk management solutions for insurers with multi-country mortality risk exposures. The third objective is to develop a method to capture waves of mortality improvement using advanced temporal correlation models. Using the resulting model, I will develop regime-dependent hedging strategies, which would allow more efficient mitigation of longevity risk. The market for longevity risk transfers is growing rapidly in Canada. In 2019 alone, four multi-billion dollar deals were closed by Canadian reinsurers. Canada's financial industry now needs the knowledge on advanced stochastic mortality modelling and risk management methods, which students will acquire in the proposed research. Canada's position in the market will also be strengthened by the research outcomes, as they are being adopted by practitioners in pension and reinsurance sectors.