Abstract
In this paper, we present and calibrate a multi-population stochastic mortality model based on latent square-root affine factors of the Cox-Ingersoll and Ross type. The model considers a generalization of the traditional actuarial mortality laws to a stochastic, multi-population and time-varying setting. We calibrate the model to fit the mortality dynamics of UK males and females over the last 50 years. We estimate the optimal states and model parameters using quasi-maximum likelihood techniques.
Highlights
Mortality laws are considered traditional actuarial models that describe the link between death probabilities and the age of the individuals
In this paper, we present and calibrate a multi-population stochastic mortality model based on latent square-root affine factors of the Cox-Ingersoll and Ross type
It is very soon after continuous-time stochastic mortality models started developing that [1] proposed the use of latent factors to generalize mortality laws to a stochastic continuoustime setting
Summary
Mortality laws are considered traditional actuarial models that describe the link between death probabilities (or the force of mortality) and the age of the individuals. [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. While several other works have used factor models to represent the evolution of mortality intensity of multiple ages simultaneously in continuous time (see [3,4], for instance), only a few, have considered non-Gaussian factors [5]. We estimate a stochastic multi-population version of the second Makeham’s law and a modification of Thiele’s law to fit the observed mortality death rates of United Kingdom females and males from 1967 to 2017 by exploiting the state-space representation of our model.
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