Presentation - International Actuarial Association

75 Pages·2013·3.28 MB·English

institut de science financiere et d’assurances laboratoire saf
UniversitéClaudeBernardLyon1
InstitutdeScienceFinancièreetd’Assurances
A New Non-parametric approach
to Smoothing and Forescating
of Mortality
Julien Tomas - Frédéric Planchet
InstitutdeScienceFinancièreetd’Assurances
LaboratoirederecherchedeSciencesActuarielleetFinancière
26/06/2013-IAALIFEColloquium-Lyon
Slide1/30
institut de science financiere et d’assurances laboratoire saf
Contents
1 Introduction 4 Numerical application
A a new robust and non-parametric The data
framework Comparison of the fits (step i.)
Two famillies of approaches Comparisons of basis functions and
2 Notation, assumption and approach corresponding coefficients (step ii.)
Notation & assumption Description of the ARIMA models
Summary of our methodology for the time-varying coefficients
The proposed models (step iii.)
3 Identifying the mortality components Projections of the time-varying
and their importance over time coefficients (step iv.)
Lee and Carter (1992) and its Graphical comparisons of the fits
variants and forecasts (step v.)
Functional principal components
analysis 5 Conclusion
Slide2/30—JulienTomas-FrédéricPlanchet—ANewNon-parametricapproachtoSmoothingandForescatingofMortality—26/06/2013-IAALIFEColloquium-Lyon
institut de science financiere et d’assurances laboratoire saf
Contents
1 Introduction 4 Numerical application
A a new robust and non-parametric The data
framework Comparison of the fits (step i.)
Two famillies of approaches Comparisons of basis functions and
2 Notation, assumption and approach corresponding coefficients (step ii.)
Notation & assumption Description of the ARIMA models
Summary of our methodology for the time-varying coefficients
The proposed models (step iii.)
3 Identifying the mortality components Projections of the time-varying
and their importance over time coefficients (step iv.)
Lee and Carter (1992) and its Graphical comparisons of the fits
variants and forecasts (step v.)
Functional principal components
analysis 5 Conclusion
Slide2/30—JulienTomas-FrédéricPlanchet—ANewNon-parametricapproachtoSmoothingandForescatingofMortality—26/06/2013-IAALIFEColloquium-Lyon
institut de science financiere et d’assurances laboratoire saf
Contents
1 Introduction 4 Numerical application
A a new robust and non-parametric The data
framework Comparison of the fits (step i.)
Two famillies of approaches Comparisons of basis functions and
2 Notation, assumption and approach corresponding coefficients (step ii.)
Notation & assumption Description of the ARIMA models
Summary of our methodology for the time-varying coefficients
The proposed models (step iii.)
3 Identifying the mortality components Projections of the time-varying
and their importance over time coefficients (step iv.)
Lee and Carter (1992) and its Graphical comparisons of the fits
variants and forecasts (step v.)
Functional principal components
analysis 5 Conclusion
Slide2/30—JulienTomas-FrédéricPlanchet—ANewNon-parametricapproachtoSmoothingandForescatingofMortality—26/06/2013-IAALIFEColloquium-Lyon
institut de science financiere et d’assurances laboratoire saf
Contents
1 Introduction 4 Numerical application
A a new robust and non-parametric The data
framework Comparison of the fits (step i.)
Two famillies of approaches Comparisons of basis functions and
2 Notation, assumption and approach corresponding coefficients (step ii.)
Notation & assumption Description of the ARIMA models
Summary of our methodology for the time-varying coefficients
The proposed models (step iii.)
3 Identifying the mortality components Projections of the time-varying
and their importance over time coefficients (step iv.)
Lee and Carter (1992) and its Graphical comparisons of the fits
variants and forecasts (step v.)
Functional principal components
analysis 5 Conclusion
Slide2/30—JulienTomas-FrédéricPlanchet—ANewNon-parametricapproachtoSmoothingandForescatingofMortality—26/06/2013-IAALIFEColloquium-Lyon
institut de science financiere et d’assurances laboratoire saf
Contents
1 Introduction 4 Numerical application
A a new robust and non-parametric The data
framework Comparison of the fits (step i.)
Two famillies of approaches Comparisons of basis functions and
2 Notation, assumption and approach corresponding coefficients (step ii.)
Notation & assumption Description of the ARIMA models
Summary of our methodology for the time-varying coefficients
The proposed models (step iii.)
3 Identifying the mortality components Projections of the time-varying
and their importance over time coefficients (step iv.)
Lee and Carter (1992) and its Graphical comparisons of the fits
variants and forecasts (step v.)
Functional principal components
analysis 5 Conclusion
Slide2/30—JulienTomas-FrédéricPlanchet—ANewNon-parametricapproachtoSmoothingandForescatingofMortality—26/06/2013-IAALIFEColloquium-Lyon
institut de science financiere et d’assurances laboratoire saf
Contents
1 Introduction 4 Numerical application
A a new robust and non-parametric The data
framework Comparison of the fits (step i.)
Two famillies of approaches Comparisons of basis functions and
2 Notation, assumption and approach corresponding coefficients (step ii.)
Notation & assumption Description of the ARIMA models
Summary of our methodology for the time-varying coefficients
The proposed models (step iii.)
3 Identifying the mortality components Projections of the time-varying
and their importance over time coefficients (step iv.)
Lee and Carter (1992) and its Graphical comparisons of the fits
variants and forecasts (step v.)
Functional principal components
analysis 5 Conclusion
Slide2/30—JulienTomas-FrédéricPlanchet—ANewNon-parametricapproachtoSmoothingandForescatingofMortality—26/06/2013-IAALIFEColloquium-Lyon
institut de science financiere et d’assurances laboratoire saf
Contents
1 Introduction 4 Numerical application
A a new robust and non-parametric The data
framework Comparison of the fits (step i.)
Two famillies of approaches Comparisons of basis functions and
2 Notation, assumption and approach corresponding coefficients (step ii.)
Notation & assumption Description of the ARIMA models
Summary of our methodology for the time-varying coefficients
The proposed models (step iii.)
3 Identifying the mortality components Projections of the time-varying
and their importance over time coefficients (step iv.)
Lee and Carter (1992) and its Graphical comparisons of the fits
variants and forecasts (step v.)
Functional principal components
analysis 5 Conclusion
Slide2/30—JulienTomas-FrédéricPlanchet—ANewNon-parametricapproachtoSmoothingandForescatingofMortality—26/06/2013-IAALIFEColloquium-Lyon
institut de science financiere et d’assurances laboratoire saf
Contents
1 Introduction 4 Numerical application
A a new robust and non-parametric The data
framework Comparison of the fits (step i.)
Two famillies of approaches Comparisons of basis functions and
2 Notation, assumption and approach corresponding coefficients (step ii.)
Notation & assumption Description of the ARIMA models
Summary of our methodology for the time-varying coefficients
The proposed models (step iii.)
3 Identifying the mortality components Projections of the time-varying
and their importance over time coefficients (step iv.)
Lee and Carter (1992) and its Graphical comparisons of the fits
variants and forecasts (step v.)
Functional principal components
analysis 5 Conclusion
Slide2/30—JulienTomas-FrédéricPlanchet—ANewNon-parametricapproachtoSmoothingandForescatingofMortality—26/06/2013-IAALIFEColloquium-Lyon
institut de science financiere et d’assurances laboratoire saf
Contents
1 Introduction 4 Numerical application
A a new robust and non-parametric The data
framework Comparison of the fits (step i.)
Two famillies of approaches Comparisons of basis functions and
2 Notation, assumption and approach corresponding coefficients (step ii.)
Notation & assumption Description of the ARIMA models
Summary of our methodology for the time-varying coefficients
The proposed models (step iii.)
3 Identifying the mortality components Projections of the time-varying
and their importance over time coefficients (step iv.)
Lee and Carter (1992) and its Graphical comparisons of the fits
variants and forecasts (step v.)
Functional principal components
analysis 5 Conclusion
Slide2/30—JulienTomas-FrédéricPlanchet—ANewNon-parametricapproachtoSmoothingandForescatingofMortality—26/06/2013-IAALIFEColloquium-Lyon