Utilisation des m\'ethodes de Lee-Carter et Log-Poisson pour l'ajustement de tables de mortalit\'e dans le cas de petits \'echantillons

TL;DR

This paper compares Lee-Carter and log-Poisson models for constructing mortality tables from small samples, focusing on extrapolation and future rate projection, with applications to real data and comparisons to logistic models.

Contribution

It introduces and applies Lee-Carter and log-Poisson models to small sample mortality data, evaluating their effectiveness for future rate projection.

Findings

Log-Poisson and Lee-Carter models effectively extrapolate mortality rates from small samples.

The models' projections are comparable to those from logistic fits.

Model caution influences the accuracy of life annuities calculations.

Abstract

The aim of this paper is to study the construction of prospective mortality tables from a low number of persons subjected to risk. The presented models are the Lee-Carter and log-Poisson methods respectively. The low number of people subjected to risk, particularly noticed for the persons who are getting on, implies the use of an extrapolation method for the mortality rates. The Lee-Carter and log-Poisson methods constitute twodimensional models, taking the year and the age into account to calculate the mortality rates. The methods suggested are applied to a real data set. The prospective tables, built in this way, allow to project the rates' evolution in the future, extrapolating the temporal constituent. And then, it allows to compare this projection with the evolution predicted for the French population in its entirety. You determine the best method through the nearness of the smoothed rates in comparison with the raw rates and essentially through the caution of these models for the life annuities' calculation. The results stemed from these methods are too confronted with the mortality rates obtained through a method of logistic fits.