Structured dispersion modelling for mortality data using a Conway--Maxwell--Poisson specification

2026-08-10

AI Summary

This study addresses the limitations of traditional mortality models, which assume a fixed discrete structure and thus struggle to capture the age- and time-varying dispersion patterns inherent in real-world data, leading to biased forecasts and poorly calibrated uncertainty. To overcome this, the paper introduces the Conway–Maxwell–Poisson (CMP) distribution into mortality modeling for the first time, establishing a unified framework capable of flexibly representing under-, equi-, and over-dispersion while allowing dispersion levels to vary heterogeneously across age and time dimensions. Employing Bayesian inference with Markov chain Monte Carlo (MCMC) methods, the approach jointly quantifies parameter, process, and distributional uncertainties. Empirical analysis of male mortality data from England and Wales demonstrates that the proposed model substantially improves the calibration of longevity risk and enhances the reliability of annuity pricing.

Abstract

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.

Problem

• dispersion
• mortality data
• Conway--Maxwell--Poisson
• longevity risk
• overdispersion

Innovation

• Conway–Maxwell–Poisson
• structured dispersion
• Bayesian modelling
• mortality forecasting
• longevity risk