The choice of sample size for mortality forecasting

A Bayesian learning approach

Research output: Contribution to journalArticleScientificpeer-review

Abstract

Forecasted mortality rates using mortality models proposed in the recent literature are sensitive to the sample size. In this paper we propose a method based on Bayesian learning to determine model-specific posterior distributions of the sample sizes. In particular, the sample size is included as an extra parameter in the parameter space of the mortality model, and its posterior distribution is obtained based on historical performance for different forecast horizons up to 20 years. Age- and gender-specific posterior distributions of sample sizes are computed. Our method is applicable to a large class of linear mortality models. As illustration, we focus on the first generation of the Lee–Carter model and the Cairns–Blake–Dowd model. Our method is applied to US and Dutch data. For both countries we find highly concentrated posterior distributions of the sample size that are gender- and age-specific. In the out-of-sample forecast analysis, the Bayesian model outperforms the original mortality models with fixed sample sizes in the majority of cases.
Original languageEnglish
Pages (from-to)153-168
Number of pages16
JournalInsurance: Mathematics & Economics
Volume63
DOIs
Publication statusPublished - 2015

Fingerprint

Bayesian Learning
Mortality
Forecasting
Sample Size
Posterior distribution
Forecast
Model
Mortality Rate
Bayesian Model
Sample size
Mortality forecasting
Bayesian learning
Parameter Space
Horizon

Keywords

  • Lee–Carter model
  • Cairns–Blake–Dowd model
  • Gibbs sampling
  • US and Dutch data
  • Linear mortality models

Cite this

@article{cf116662964e4e6698b5dcf103e76624,
title = "The choice of sample size for mortality forecasting: A Bayesian learning approach",
abstract = "Forecasted mortality rates using mortality models proposed in the recent literature are sensitive to the sample size. In this paper we propose a method based on Bayesian learning to determine model-specific posterior distributions of the sample sizes. In particular, the sample size is included as an extra parameter in the parameter space of the mortality model, and its posterior distribution is obtained based on historical performance for different forecast horizons up to 20 years. Age- and gender-specific posterior distributions of sample sizes are computed. Our method is applicable to a large class of linear mortality models. As illustration, we focus on the first generation of the Lee–Carter model and the Cairns–Blake–Dowd model. Our method is applied to US and Dutch data. For both countries we find highly concentrated posterior distributions of the sample size that are gender- and age-specific. In the out-of-sample forecast analysis, the Bayesian model outperforms the original mortality models with fixed sample sizes in the majority of cases.",
keywords = "Lee–Carter model, Cairns–Blake–Dowd model, Gibbs sampling, US and Dutch data, Linear mortality models",
author = "Hong Li and {De Waegenaere}, Anja and Bertrand Melenberg",
note = "Special Issue: Longevity Nine - the Ninth International Longevity Risk and Capital Markets Solutions Conference",
year = "2015",
doi = "10.1016/j.insmatheco.2015.03.024",
language = "English",
volume = "63",
pages = "153--168",
journal = "Insurance: Mathematics & Economics",
issn = "0167-6687",
publisher = "Elsevier Science BV",

}

The choice of sample size for mortality forecasting : A Bayesian learning approach. / Li, Hong; De Waegenaere, Anja; Melenberg, Bertrand.

In: Insurance: Mathematics & Economics, Vol. 63, 2015, p. 153-168.

Research output: Contribution to journalArticleScientificpeer-review

TY - JOUR

T1 - The choice of sample size for mortality forecasting

T2 - A Bayesian learning approach

AU - Li, Hong

AU - De Waegenaere, Anja

AU - Melenberg, Bertrand

N1 - Special Issue: Longevity Nine - the Ninth International Longevity Risk and Capital Markets Solutions Conference

PY - 2015

Y1 - 2015

N2 - Forecasted mortality rates using mortality models proposed in the recent literature are sensitive to the sample size. In this paper we propose a method based on Bayesian learning to determine model-specific posterior distributions of the sample sizes. In particular, the sample size is included as an extra parameter in the parameter space of the mortality model, and its posterior distribution is obtained based on historical performance for different forecast horizons up to 20 years. Age- and gender-specific posterior distributions of sample sizes are computed. Our method is applicable to a large class of linear mortality models. As illustration, we focus on the first generation of the Lee–Carter model and the Cairns–Blake–Dowd model. Our method is applied to US and Dutch data. For both countries we find highly concentrated posterior distributions of the sample size that are gender- and age-specific. In the out-of-sample forecast analysis, the Bayesian model outperforms the original mortality models with fixed sample sizes in the majority of cases.

AB - Forecasted mortality rates using mortality models proposed in the recent literature are sensitive to the sample size. In this paper we propose a method based on Bayesian learning to determine model-specific posterior distributions of the sample sizes. In particular, the sample size is included as an extra parameter in the parameter space of the mortality model, and its posterior distribution is obtained based on historical performance for different forecast horizons up to 20 years. Age- and gender-specific posterior distributions of sample sizes are computed. Our method is applicable to a large class of linear mortality models. As illustration, we focus on the first generation of the Lee–Carter model and the Cairns–Blake–Dowd model. Our method is applied to US and Dutch data. For both countries we find highly concentrated posterior distributions of the sample size that are gender- and age-specific. In the out-of-sample forecast analysis, the Bayesian model outperforms the original mortality models with fixed sample sizes in the majority of cases.

KW - Lee–Carter model

KW - Cairns–Blake–Dowd model

KW - Gibbs sampling

KW - US and Dutch data

KW - Linear mortality models

U2 - 10.1016/j.insmatheco.2015.03.024

DO - 10.1016/j.insmatheco.2015.03.024

M3 - Article

VL - 63

SP - 153

EP - 168

JO - Insurance: Mathematics & Economics

JF - Insurance: Mathematics & Economics

SN - 0167-6687

ER -