英文标题：
《Stochastic mortality models: An infinite dimensional approach》
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作者：
Stefan Tappe and Stefan Weber
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最新提交年份：
2019
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英文摘要：
Demographic projections of future mortality rates involve a high level of uncertainty and require stochastic mortality models. The current paper investigates forward mortality models driven by a (possibly infinite dimensional) Wiener process and a compensated Poisson random measure. A major innovation of the paper is the introduction of a family of processes called forward mortality improvements which provide a flexible tool for a simple construction of stochastic forward mortality models. In practice, the notion of mortality improvements are a convenient device for the quantification of changes in mortality rates over time that enables, for example, the detection of cohort effects. We show that the forward mortality rates satisfy Heath-Jarrow-Morton-type consistency conditions which translate to the forward mortality improvements. While the consistency conditions of the forward mortality rates are analogous to the classical conditions in the context of bond markets, the conditions of the forward mortality improvements possess a different structure: forward mortality models include a cohort parameter besides the time horizon; these two dimensions are coupled in the dynamics of consistent models of forwards mortality improvements. In order to obtain a unified framework, we transform the systems of It\\^o-processes which describe the forward mortality rates and improvements: in contrast to term-structure models, the corresponding stochastic partial differential equations (SPDEs) describe the random dynamics of two-dimensional surfaces rather than curves.
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中文摘要：
未来死亡率的人口预测涉及高度不确定性，需要随机死亡率模型。本文研究由（可能无限维）维纳过程和补偿泊松随机测度驱动的正向死亡率模型。本文的一个主要创新是引入了一系列称为前向死亡率改进的过程，这为简单构建随机前向死亡率模型提供了一个灵活的工具。在实践中，死亡率改善的概念是一种方便的方法，可以量化死亡率随时间的变化，例如，可以检测队列效应。我们证明，远期死亡率满足Heath-Jarrow-Morton型一致性条件，这转化为远期死亡率的提高。虽然远期死亡率的一致性条件类似于债券市场中的经典条件，但远期死亡率改善的条件具有不同的结构：远期死亡率模型除了时间范围外，还包括一个队列参数；这两个维度在远期死亡率改善的一致模型的动力学中是耦合的。为了获得一个统一的框架，我们将描述正向死亡率和改进的It过程系统进行转换：与项结构模型相比，相应的随机偏微分方程（SPDE）描述的是二维曲面而非曲线的随机动力学。
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分类信息：

一级分类：Mathematics 数学
二级分类：Probability 概率
分类描述：Theory and applications of probability and stochastic processes: e.g. central limit theorems, large deviations, stochastic differential equations, models from statistical mechanics, queuing theory
概率论与随机过程的理论与应用：例如中心极限定理，大偏差，随机微分方程，统计力学模型，排队论
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一级分类：Quantitative Finance 数量金融学
二级分类：Pricing of Securities 证券定价
分类描述：Valuation and hedging of financial securities, their derivatives, and structured products
金融证券及其衍生产品和结构化产品的估值和套期保值
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