基于康威-麦克斯韦-泊松（Conway--Maxwell--Poisson，CMP）规范的死亡率数据结构化离散度建模
Structured dispersion modelling for mortality data using a Conway--Maxwell--Poisson specification
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中文总结 AI 辅助
该研究针对死亡率模型离散度结构固定的缺陷，提出采用康威-麦克斯韦-泊松分布的灵活贝叶斯框架，经实证验证其可捕捉年龄和时间相关的离散度异质性，对长寿风险与年金定价有重要意义。
中文摘要 AI 辅助
尝试捕捉离散度的死亡率模型通常假设离散度结构固定，该假设在实践中很少满足，可能导致不确定性校准错误和预测性能不佳。本文引入了一个灵活框架，使用康威-麦克斯韦-泊松（Conway--Maxwell--Poisson，CMP）分布显式建模死亡率数据的离散度，该分布在统一规范内可容纳欠离散、等离散和过离散。该框架不施加全局离散度参数，而是允许离散度的类型和程度随年龄和时间变化，从而捕捉到更简单模型可能忽略的结构异质性。贝叶斯公式将离散度视为未知量，其先验结构可连贯地传播参数、过程和分布不确定性。估计通过马尔可夫链蒙特卡洛（Markov chain Monte Carlo，MCMC）方法进行。使用英格兰和威尔士男性的经验死亡数据，我们表明死亡率计数的变异性在不同年龄和不同时间段存在显著差异，这对长寿风险的校准和年金产品的定价具有重要意义。
英文摘要
Mortality models that attempt to capture dispersion typically assume a fixed dispersion structure, an assumption that is rarely satisfied in practice and that can lead to miscalibrated uncertainty and poor predictive performance. In this paper, we introduce a flexible framework for explicitly modelling dispersion in mortality data using the Conway--Maxwell--Poisson (CMP) distribution, which accommodates underdispersion, equidispersion, and overdispersion within a unified specification. Rather than imposing a global dispersion parameter, the framework allows both the type and degree of dispersion to vary by age and over time, thus capturing structural heterogeneity that simpler models may overlook. A Bayesian formulation treats dispersion as unknown, with prior structures that coherently propagate parameter, process, and distributional uncertainty. Estimation is carried out via Markov chain Monte Carlo (MCMC) methods. Using empirical death data for males in England and Wales, we show that variability in mortality counts differs substantially across ages and across time periods. This has meaningful implications for the calibration of longevity risk and the pricing of annuity products.
