Modeling of mortality rates, hedging of longevity and mortality risks, and pricing of mortality-linked securities

对死亡率的变化/动态进行建模对于社会福利计划、人寿保险公司的偿付能力以及整个社会都至关重要。死亡率是塑造一个国家人口结构的一个重要因素，而人口结构反过来又影响到许多行业的增长前景。退休计划和长期护理系统也需要考虑死亡率的动态，因为收入和福利支出取决于死亡率。死亡率也是决定人寿保险和年金产品保费和准备金的关键因素之一。因此，死亡率的建模是一个非常重要的问题。有证据表明，在过去的几十年里，人类死亡率逐渐提高。如果不能适当衡量死亡率的下降趋势，就会低估年金和养老金产品的保费和准备金，从而使年金和养老金提供者面临财务困境的风险。由于长期准确预测死亡率是极其困难的，年金和养老金提供者需要采取一些策略和/或购买适当的与死亡率挂钩的证券来对冲长寿风险。与由金融研究人员广泛创建并在金融市场交易的利息证券不同，与死亡挂钩的证券很少发行和交易。面对死亡率提高的现象，年金和养老金提供者现在需要更多与死亡率挂钩的证券作为对冲长寿风险的工具。 拟议的研究计划涉及死亡率的建模、对长寿和死亡风险的对冲，以及与死亡挂钩的证券的定价。在该项目中，我打算重点关注以下三个主要目标： ·对于死亡率的建模，我想提出关系模型(死亡率建模中的关系模型将一个死亡率序列与另一个具有一定关系的死亡率序列联系起来)及其变化，用于样本内死亡率拟合和样本外死亡率预测；模型还将涉及一些重要特征，包括队列效应、跳跃成分、共同冲击、相关性、随机过程和时间序列。 ·为了对冲死亡和长寿风险，我将把我之前提出的死亡持续期和凸度应用于三种或更多保险产品的投资组合，以及其他一些与死亡挂钩的证券；还将详细研究分别产生对冲死亡和长寿风险最佳表现的权重的最优问题。 ·对于基于著名的Lee-Carter模型或建议的关系模型的现有死亡率挂钩证券的定价，将考虑第一个目标中的特征以反映一种或多种不同的情况；将提出新的死亡率挂钩证券，其灵感来自现有的基于利率的衍生品，即使涉及高级金融数学，其定价也将在很大程度上得到调查。 关系模型及其变体是建模死亡率和对冲死亡率/寿命风险的全新方法。它们易于实现，在死亡率拟合/预测中具有良好的性能，并且由于它们的简单性和有效性以及两个死亡率序列之间的关系而提供了许多潜在的应用。这项研究计划的完成将帮助人寿保险公司、社会保障和退休福利提供者以及相关行业减少因死亡/长寿风险而导致财务困境的可能性。我期待着在死亡率研究领域做出重大贡献。

Modeling the changes/dynamics of mortality rates is critical to the social benefit programs, solvency of life insurers, and the society as a whole. Mortality is a significant factor in shaping the population structure of a country that in turn affects the growth prospects of many industries. Retirement programs and long-term care systems need to consider the dynamics of mortality rates as well since incomes and benefit outgoes depend on mortality. Mortality is also one of the key factors in determining the premiums and reserves of life insurance and annuity products. Therefore, modeling of mortality is a very important issue. Evidence shows that human mortality rates improve gradually over the past decades. A failure to appropriately measure the downward trends in mortality rates would underestimate the premiums and reserves for annuity and pension products and then expose annuity and pension providers to the risks of financial distress. Since forecasting mortality rates accurately for a long period is extremely difficult, annuity and pension providers need to hedge the longevity risk by adopting some strategies and/or buying appropriate mortality-linked securities. Unlike interest-based securities which are widely created by financial researchers and traded in financial markets, mortality-linked securities have been rarely issued and traded. Facing the phenomenon of mortality improvement, annuity and pension providers now are in need of more mortality-linked securities as instruments for hedging longevity risk. The proposed research program pertains to modeling of mortality rates, hedging of longevity and mortality risks, and pricing of mortality-linked securities. In the project, I intend to focus on the following three main objectives: • For modeling of mortality, I would like to propose relational models (a relational model in modeling of mortality rates connects one mortality sequence to the other with some relationship) and its variations for in-sample mortality fitting and out-of-sample mortality forecasting; some important features including the cohort effect, a jump component, a common shock, dependency, stochastic processes and time series will also be involved in the models. • For hedging of mortality and longevity risks, I will apply my previously proposed mortality durations and convexities to a portfolio of three or more insurance products and to some other mortality-linked securities; the optimal problems regarding the weights producing the best performance of hedging mortality and longevity risks, respectively, will also be studied in details. • For pricing of existing mortality-linked securities based on the well-known Lee-Carter model or the proposed relational models, the features in the first objective will be considered to reflect one or more of various situations; new mortality-linked securities inspired from existing interest-based derivative ones will be proposed, and their pricing even though advanced financial mathematics is involved will be investigated to a great extent. The relational models and their variations are brand-new approaches to modeling mortality rates and hedging mortality/longevity risks. They are easy to implement, have good performance in mortality fitting/forecasting, and offer many potential applications due to their simplicity and effectiveness plus a relationship between two mortality sequences. The completion of this research program will help life insurers, social security and retirement benefit providers, and relevant industries reduce the possibilities of financial distress caused by mortality/longevity risks. I expect to make significant contributions to the field of mortality study.