A continuous-time stochastic model for the mortality surface of multiple populations

Abstract

We formulate, study and calibrate a continuous-time model for the joint evolution of the mortality surface of multiple populations. We model the mortality intensity by age and population as a mixture of stochastic latent factors, that can be either population-specific or common to all populations. These factors are described by affine time-(in)homogenous stochastic processes. Traditional, deterministic mortality laws can be extended to multi-population stochastic counterparts within our framework. We detail the calibration procedure when factors are Gaussian, using centralized data-fusion Kalman filter. We provide an application based on the mortality of UK males and females. Although parsimonious, the specification we calibrate provides a good fit of the observed mortality surface (ages 0-99) of both sexes between 1960 and 2013.

Geographical Diversification and Longevity Risk Mitigation in Annuity Portfolios

“…Both the basis-risk model and the one we are going to develop below are a stochastic extension of the deterministic Gompertz mortality law, a benchmark in the classical modeling of mortality arrival rates. Jevtić and Regis (2019) and Sherris et al (2020) use stochastic processes belonging to the affine class to model the mortality of multiple cohorts and populations. While these papers propose applications based on the use of three Brownian risk sources, we assume as many dependent risk factors as domestic generations and an idiosyncratic source that drives the mortality intensity of the foreign population.…”

A Square-Root Factor-Based Multi-Population Extension of the Mortality Laws

“…In particular, [1] calibrated the one-year death probabilities of several ages of the Dutch population to 2or 3-factor Gaussian models that extended the first and second Makeham's and Thiele's laws to a stochastic setting. The authors of [2] built on a similar setup to propose a general multi-population stochastic extension of mortality laws. There, the mortality intensities of several populations were affine functions of affine latent factors.…”

“…Population-specific parameters interact with such factors to reproduce the age-mortality relation. While the setting described in [2] was very general, the implementation was restricted to the use of Gaussian factors. The Gaussian factors have the advantage of being easier to calibrate.…”

“…That is a relevant shortcoming, for instance, for annuity pricing purposes. In their work, [2] described the application of a 4-population 3-factor law, they estimated through the use of a sequential Kalman filter. In this paper, we advance the previous work and focus on the case in which factors are non-Gaussian, which has not been previously undertaken in the actuarial literature.…”

The dependency premium based on a multifactor model for dependent mortality data

“…Kleinow (2015) introduces the Common Age Effect Model (CAE model), where the common age effect in age-period model for multiple populations is estimated by a common principal component analysis. A full review of the different multiple population models in discrete time is provided by Villegas et al (2017); multi factor stochastic mortality models in continuous time for multiple population are proposed by Jevtic and Regis (2016).…”