Skip to main content
Fachgebiete
Automobil + Motoren Bauwesen + Immobilien Business IT + Informatik Elektrotechnik + Elektronik Energie + Nachhaltigkeit Finance + Banking Management + Führung Marketing + Vertrieb Maschinenbau + Werkstoffe Versicherung + Risiko
DE
EN
Bücher
Zeitschriften
Themenseiten
Organisationspsychologie Projektmanagement Marketing Smart Manufacturing
Weitere Formate
Podcasts Webinare Technik Webinare Wirtschaft Kongresse Veranstaltungskalender Awards
Jetzt Einzelzugang starten
Zugang für Unternehmen
Referenzkunden
SLX-Digitalkonferenz: Zukunftswerkstatt 2024

Mehr Umsatz mit Top-Kontakten

Am 7. Mai erfahren Sie, wie Vertriebsteams Leadgenerierung, Leadnurturing und Leadstrategien effizient steuern können.
Erweiterte Suche
Anmelden
nach oben
European Actuarial Journal
Erschienen in: European Actuarial Journal 2/2017

14.10.2017 | Original Research Paper

Producing the Dutch and Belgian mortality projections: a stochastic multi-population standard

verfasst von: Katrien Antonio, Sander Devriendt, Wouter de Boer, Robert de Vries, Anja De Waegenaere, Hok-Kwan Kan, Egbert Kromme, Wilbert Ouburg, Tim Schulteis, Erica Slagter, Marco van der Winden, Corné van Iersel, Michel Vellekoop

Erschienen in: European Actuarial Journal | Ausgabe 2/2017

Einloggen

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config
loading …

Abstract

The quantification of longevity risk in a systematic way requires statistically sound forecasts of mortality rates and their corresponding uncertainty. Actuarial associations have a long history and continue to play an important role in the development, application and dispersion of mortality projections for the countries they represent. This paper gives an in depth presentation and discussion of the mortality projections as published by the Dutch (in 2014) and Belgian (in 2015) actuarial associations. The goal of these institutions was to publish a stochastic mortality projection model in line with both rigorous standards of state-of-the-art academic work as well as the requirements of practical work such as robustness and transparency. Constructed by a team of authors from both academia and practice, the developed mortality projection standard is a Li and Lee type multi-population model. To project mortality, a global Western European trend and a country-specific deviation from this trend are jointly modelled with a bivariate time series model. We motivate and document all choices made in the model specification, calibration and forecasting process as well as the model selection strategy. We show the model fit and mortality projections and illustrate the use of the model in several pension-related applications.
Nächster Artikel Machine learning techniques for mortality modeling

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

Jetzt informieren
Fußnoten
1
We refer to Chapter 4. The financial impact of longevity risk.
 
2
We refer to Part II: Long-term projections of age-related expenditure and unemployment benefits.
 
3
See Table II.1.15 in European Commission (DG ECFIN) and Economic Policy Committee (Ageing Working Group) [27], p. 79.
 
4
See, for example, the ‘Algemene Ouderdomswet’ (AOW-law): http://​wetten.​overheid.​nl/​BWBR0002221/​. The definition of period life expectancy is given in Sect. 5.1.
 
6
See, for example, their 2014 and 2015 reports: Commissie Pensioenhervorming 2020–2040 [14, 15].
 
7
More history on the \({\textsf {CMI}}\) can be found in Institute of Actuaries and Faculty of Actuaries [33], pp. 1–5.
 
8
For example, the 2012 IAM and IAR, GAM–83 and GAR–94, see National Association of Insurance Commissioners [41], section 3.
 
9
A complete description of the model is in Koninklijk Actuarieel Genootschap [36].
 
10
We refer to Institute and Faculty of Actuaries [32] and Society of Actuaries [48] for more information.
 
11
The multi-population models in this report consist of various combinations of mortality models for the multi-population trend and the country-specific deviation.
 
13
For example, these definitions are used by ‘Centraal Bureau voor Statistiek’ (\({\textsf {CBS}}\), http://​www.​cbs.​nl/​en-GB/​menu/​home/​default.​htm?​Languageswitch=​on) in The Netherlands and ‘Algemene Directie Statistiek—Statistics Belgium’ (\({\textsf {ADS}}\), http://​statbel.​fgov.​be/​en/​statistics/​figures/​) in Belgium.
 
14
We use the \({\textsf {CBS}}\) definitions where the age-time subscript ‘x, t’ refers to people born in year \(t-x\). Other institutions, such as the \({\textsf {ADS}}\), use ‘x, t’ to refer to people born in year \(t-x-1\).
 
15
This mortality database is available at http://​www.​mortality.​org.
 
16
Source: World Bank Data for 2013 on \({\textsf {GDP}}\) per capita in US dollar, http://​data.​worldbank.​org/​indicator/​NY.​GDP.​PCAP.​CD.
 
17
See bottom of page 6 in the \({\textsf {HMD}}\) protocol: http://​www.​mortality.​org/​Public/​Docs/​MethodsProtocol.​pdf.
 
18
Since we reproduce the results and forecasts as published by \({\textsf {KAG}}\) on 9 September 2014 and by \({\textsf {IA}\vert \textsf {BE}}\) on 18 February 2015 we use the data used by the authors of these publications, as downloaded on 29 May 2014.
 
19
On 30 December 2015, data until 2012 for both The Netherlands and Belgium was available on \({\textsf {HMD}}\). This data was used to stay as close as possible to the original dataset used by \({\textsf {KAG}}\) and \({\textsf {IA}\vert \textsf {BE}}\).
 
21
The number of deaths per year, age and gender are available at http://​alturl.​com/​dz7mc.
 
22
Data from, for example, \({\textsf {CBS}}\) shows that the yearly net migration in recent years is around 0.2% of the total population and for specific ages is almost always less than 2%. We consider these effects small enough to not have a significant impact on the calculations. Population data from http://​statline.​cbs.​nl/​Statweb/​publication/​?​DM=​SLNL&​PA=​7461BEV&​D1=​0&​D2=​1-2&​D3=​1-100&​D4=​45-66&​HDR=​G1,G3,T&​STB=​G2&​VW=​T and migration data from http://​statline.​cbs.​nl/​Statweb/​publication/​?​DM=​SLNL&​PA=​03742&​D1=​3&​D2=​1-2&​D3=​1-96&​D4=​0&​D5=​0&​D6=​a&​HDR=​G3,T,G1,G5&​STB=​G4,G2&​VW=​T.
 
23
Proper scoring rules are out-of-sample evaluation criteria. They are used to assess model predictions by allocating a score for each prediction, based on its accuracy and sharpness. Examples of these scores are the predictive deviance, the squared Pearson residuals or the Dawid–Sebastiani scoring rule from Dawid and Sebastiani [19].
 
25
The Pearson residuals for the Poisson regression in our model are defined as \(\frac{d_{x,t}^{(c)} - E_{x,t}^{(c)}\hat{\mu }^{(c)}_{x,t}}{\sqrt{E_{x,t}^{(c)}\hat{\mu }^{(c)}_{x,t}}}\).
 
26
In R we use Seemingly Unrelated Regression through the package systemfit, we use the function systemfit with options method=“SUR” and methodResidCov=“noDfCor”.
 
28
The Dutch calibration for this backtest initially led to an unstable \({\textsf {AR}}\)(1) parameter in the country specific time series: \(a>1\). The results shown here are with an inequality constrained calibration for the time series to keep them stationary.
 
29
We note that the \({\textsf {KAG}}\) uses a slightly different definition of life expectancies, available on page 34 of Koninklijk Actuarieel Genootschap [37].
 
30
The interest rate i is set to a constant 1% and inflation g is ignored, i.e. 0%. The red band in the left panel of Fig. 13 are period calculations of \(\text{PV}_{65,t}(10{,}000)\), obtained by replacing \(q_{x+l,t+l}\) in (31) with \(q_{x+l,t}\).
 
31
The age at which one reaches a full career, i.e. the normal pension age, can be different from person to person depending, amongst others, on the age one starts working and any period of inactivity on the way.
 
32
The quantities are actually ‘curtate’ cohort life expectancies, see, for example, Dickson et al. [23].
 
33
This is the benefit one would receive in case of retiring at normal pension age \(x_n\) in year \(t_n\) but calculated using the individual’s situation regarding pension variables (such as career length, social security status,\(\ldots\)) at age \(x_r\) in year \(t_r\). Thus, only the timing/mortality aspect of benefits is taken into account.
 
34
As such, it is possible that one person has a normal pension age of 67 while another has a normal pension age of 62, depending on career length, type of profession, etc. See Commissie Pensioenhervorming 2020–2040 [14] for more information.
 
35
Since there are 10,000 simulations for the reference point and 10,000 simulations for all period life expectancies from 2014 onwards, the quantiles were calculated on \(10{,}000\times 10{,}000\) evaluations of the correction factor \(\gamma\). For the year 2013, only 10,000 evaluations were necessary since \(e_{60,2013}^{\text{per}}\) is known and observed.
 
36
Of course, the benefit \(B_{x_r,t_r}\) is still dependent on the situation of the underlying individual, but the numerator numerator of the actuarial correction \(\gamma\) in (33) is now the same for the whole population.
 
37
This section is based on the Dutch retirement law (AOW-law) as consulted on 29 April 2016: http://​wetten.​overheid.​nl/​BWBR0002221/​.
 
38
This approach is slightly different from the unisex methodology of \({\textsf {CBS}}\).
 
39
The value 20.26 is obtained by filling in \(P_{2021} = 67\) in (35) and simplifying, leading to \(e_{65,2022}^{\text{per}}\) being compared with \(18.26+2\). If the predicted \({\textsf {PLE}}\) is significantly higher than this number (e.g. 8 months higher), subsequent yearly three month increases are necessary to compensate for this difference.
 
40
See Appendix B of the English version of the \({\textsf {KAG}}\) publication: http://​www.​ag-ai.​nl/​view.​php?​action=​view&​Pagina_​Id=​625.
 
41
For example, all people in the portfolio aged 40-49 are in class \(c=2\) and have their age rounded to \(x_c=40\). This is assumed because we do not have full portfolio data but only exposures per age class.
 
Literatur
1.
Albrecher H, Embrechts P, Filipović D, Harrison G, Koch P, Loisel S, Vanini P, Wagner J (2016) Old-age provision: past, present, future. Eur Actuar J 6(2):287–306MathSciNetCrossRefMATH
2.
3.
4.
Barrieu P, Bensusan H, El Karoui N, Hillairet C, Loisel S, Ravanelli C, Salhi Y (2012) Understanding, modelling and managing longevity risk: key numbers and main challenges. Scand Actuar J 3:203–231CrossRefMATH
5.
Börger M, Fleischer D, Kuksin N (2014) Modeling the mortality trend under modern solvency regimes. ASTIN Bull 44(1):1–38MathSciNetCrossRef
6.
Brouhns N, Denuit M, Vermunt J (2002) A Poisson log-bilinear regression approach to the construction of projected life tables. Insur Math Econ 31:373–393CrossRefMATH
7.
8.
Cairns A, Blake D, Dowd K (2006) A two-factor model for stochastic mortality with parameter uncertainty: theory and calibration. J Risk Insur 73:687–718CrossRef
9.
Cairns A, Blake D, Dowd K, Coughlan G, Epstein D, Ong A, Balevich I (2009) A quantitative comparison of stochastic mortality models using data from England and Wales and the United States. N Am Actuar J 13(1):1–35MathSciNetCrossRef
10.
Cairns A, Blake D, Dowd K, Kessler A (2016) Phantoms never die: living with unreliable population data. J R Stat Soc Ser A (Stat Soc) 179(4):975–1005MathSciNetCrossRef
11.
12.
Carter L, Lee R (1992) Forecasting demographic components: modeling and forecasting US sex differentials in mortality. Int J Forecast 8:393–411CrossRef
13.
14.
Commissie Pensioenhervorming 2020–2040 (2014). Een sterk en betrouwbaar sociaal contract. Voorstellen van de Commissie Pensioenhervorming 2020–2040 voor een structurele hervorming van de pensioenstelsels. http://​www.​pensioen2040.​belgie.​be
15.
Commissie Pensioenhervorming 2020–2040 (2015) Zware beroepen, deeltijds pensioen en eerlijke flexibiliteit in het pensioensysteem. Aanvullend advies van de Commissie Pensioenhervorming 2020–2040. http://​www.​pensioen2040.​belgie.​be
16.
17.
D’Amato V, Haberman S, Piscopo G, Russolillo M, Trapani L (2014) Detecting common longevity trends by a multiple population approach. N Am Actuar J 18(1):139–149MathSciNetCrossRefMATH
18.
D’Amato V, Haberman S, Piscopo G, Russolillo M, Trapani L (2016) Multiple mortality modeling in a Poisson Lee–Carter framework. Commun Stat Theory Methods 45(6):1723–1732MathSciNetCrossRefMATH
19.
20.
De Waegenaere A, Melenberg B, Boonen T (2012) Het koppelen van de pensioenleeftijd en pensioenaanspraken aan de levensverwachting. Netspar Design Papers, 12
21.
Denuit M, Goderniaux A-C (2005) Closing and projecting life tables using log-linear models. Bull Swiss Assoc Actuar 1:29–48MathSciNetMATH
22.
Devolder P, Maréchal X (2007) Réforme du régime belge de pension légale basée sur la longévité. Belg Actuar Bull 7:34–38MathSciNet
23.
Dickson D, Hardy M, Waters H (2009) Actuarial mathematics for life contingent risks. Cambridge University Press, CambridgeCrossRefMATH
24.
Doray L (2008) Inference for the logistic-type models for the force of mortality. In: Living to 100 and beyond, SOA Monograph M-LI08-01, pp 1–18
25.
Dowd K, Cairns A, Blake D, Coughlan G, Epstein D, Khalaf-Allah M (2010) Backtesting stochastic mortality models. N Am Actuar J 14(3):281–298MathSciNetCrossRefMATH
26.
Enchev V, Kleinow T, Cairns A (2017) Multi-population mortality models: fitting, forecasting and comparisons. Scand Actuar J 2017(4):319–342MathSciNetCrossRef
27.
28.
29.
30.
Hyndman R, Booth H, Yasmeen F (2013) Coherent mortality forecasting: the product-ratio method with functional time series models. Demography 50(1):261–283CrossRef
31.
32.
33.
34.
Kannistö V (1992) Development of the oldest-old mortality, 1950–1990: evidence from 28 developed countries. Odense University Press, Odense
35.
36.
37.
38.
Lee R, Carter L (1992) Modeling and forecasting the time series of US mortality. J Am Stat Assoc 87:659–671MATH
39.
Li J (2013) A Poisson common factor model for projecting mortality and life expectancy jointly for females and males. Popul Stud J Demogr 67(1):111–126CrossRef
40.
Li N, Lee R (2005) Coherent mortality forecasts for a group of populations: an extension of the Lee–Carter method. Demography 42(3):575–594CrossRef
41.
42.
Niu G, Melenberg B (2014) Trends in mortality decrease and economic growth. Demography 51(5):1755–1773CrossRef
43.
Pitacco E, Denuit M, Haberman S, Olivieri A (2009) Modeling longevity dynamics for pensions and annuity business. Oxford University Press, OxfordMATH
44.
45.
Renshaw A, Haberman S (2006) A cohort-based extension to the Lee–Carter model for mortality reduction factors. Insur Math Econ 38:556–570CrossRefMATH
46.
47.
Shang H (2016) Mortality and life expectancy forecasting for a group of populations in developed countries: a multilevel functional data method. Ann Appl Stat 10(3):1639–1672MathSciNetCrossRefMATH
48.
49.
50.
Van Berkum F, Antonio K, Vellekoop M (2016) The impact of multiple structural changes on mortality predictions. Scand Actuar J 2016(7):581–603MathSciNetCrossRef
51.
Villegas A, Haberman S (2014) On the modeling and forecasting of socioeconomic mortality differentials: an application to deprivation and mortality in England. N Am Actuar J 18(1):168–193MathSciNetCrossRef
Metadaten
Titel
Producing the Dutch and Belgian mortality projections: a stochastic multi-population standard
verfasst von
Katrien Antonio
Sander Devriendt
Wouter de Boer
Robert de Vries
Anja De Waegenaere
Hok-Kwan Kan
Egbert Kromme
Wilbert Ouburg
Tim Schulteis
Erica Slagter
Marco van der Winden
Corné van Iersel
Michel Vellekoop
Publikationsdatum
14.10.2017
Verlag
Springer Berlin Heidelberg
Erschienen in
European Actuarial Journal / Ausgabe 2/2017
Print ISSN: 2190-9733
Elektronische ISSN: 2190-9741
DOI
https://doi.org/10.1007/s13385-017-0159-x

Weitere Artikel der Ausgabe 2/2017

European Actuarial Journal 2/2017 Zur Ausgabe

Original Research Paper

Machine learning techniques for mortality modeling

Original Research Paper

On optimal dividends with penalty payments in the Cramér–Lundberg model

Original Research Paper

Applications of the central limit theorem for pricing Cliquet-style options

Original Research Paper

A compound trend renewal model for medical/professional liabilities

Original Research Paper

Solvency II solvency capital requirement for life insurance companies based on expected shortfall

Original Research Paper

Utility indifference pricing of insurance catastrophe derivatives