A comparison of the Lee–Carter model and AR–ARCH model for forecasting mortality rates

2012 ◽  
Vol 50 (1) ◽  
pp. 85-93 ◽  
Author(s):  
Rosella Giacometti ◽  
Marida Bertocchi ◽  
Svetlozar T. Rachev ◽  
Frank J. Fabozzi
Keyword(s):  
Mortality Rates ◽  
Arch Model ◽  
Carter Model

scholarly journals Do Different Models Induce Changes in Mortality Indicators? That Is a Key Question for Extending the Lee-Carter Model

2021 ◽  
Vol 18 (4) ◽  
pp. 2204
Author(s):  
Ana Debón ◽  
Steven Haberman ◽  
Francisco Montes ◽  
Edoardo Otranto
Keyword(s):  
Historical Data ◽  
Mortality Rates ◽  
Parametric Model ◽  
Mortality Data ◽  
Block Bootstrap ◽  
Functional Anova ◽  
Model Block ◽  
The Usa ◽  
Data Constraints ◽  
Carter Model

The parametric model introduced by Lee and Carter in 1992 for modeling mortality rates in the USA was a seminal development in forecasting life expectancies and has been widely used since then. Different extensions of this model, using different hypotheses about the data, constraints on the parameters, and appropriate methods have led to improvements in the model’s fit to historical data and the model’s forecasting of the future. This paper’s main objective is to evaluate if differences between models are reflected in different mortality indicators’ forecasts. To this end, nine sets of indicator predictions were generated by crossing three models and three block-bootstrap samples with each of size fifty. Later the predicted mortality indicators were compared using functional ANOVA. Models and block bootstrap procedures are applied to Spanish mortality data. Results show model, block-bootstrap, and interaction effects for all mortality indicators. Although it was not our main objective, it is essential to point out that the sample effect should not be present since they must be realizations of the same population, and therefore the procedure should lead to samples that do not influence the results. Regarding significant model effect, it follows that, although the addition of terms improves the adjustment of probabilities and translates into an effect on mortality indicators, the model’s predictions must be checked in terms of their probabilities and the mortality indicators of interest.

A neural network extension of the Lee–Carter model to multiple populations

2019 ◽  
pp. 1-21 ◽  
Author(s):  
Ronald Richman ◽  
Mario V. Wüthrich
Keyword(s):  
Representation Learning ◽  
Mortality Rates ◽  
Model Structure ◽  
Optimal Model ◽  
Single Population ◽  
Basic Approach ◽  
Multiple Populations ◽  
Forecasting Performance ◽  
Out Of Sample ◽  
Carter Model

Abstract The Lee–Carter (LC) model is a basic approach to forecasting mortality rates of a single population. Although extensions of the LC model to forecasting rates for multiple populations have recently been proposed, the structure of these extended models is hard to justify and the models are often difficult to calibrate, relying on customised optimisation schemes. Based on the paradigm of representation learning, we extend the LCmodel to multiple populations using neural networks, which automatically select an optimal model structure. We fit this model to mortality rates since 1950 for all countries in the Human Mortality Database and observe that the out-of-sample forecasting performance of the model is highly competitive.

scholarly journals The Heteroscedasticity Impact on Actuarial Science: Lee Carter Error Simulation

2018 ◽  
Vol 2 (1) ◽  
pp. 44-55
Author(s):  
Olgerta Idrizi ◽  
Besa Shahini
Keyword(s):  
Financial Risk ◽  
Population Data ◽  
Mortality Rates ◽  
Model Specification ◽  
Insurance Companies ◽  
Actuarial Science ◽  
Demographic Risk ◽  
The Impact ◽  
Error Simulation ◽  
Carter Model

Abstract C19 Life insurance companies deal with two fundamental types of risks when issuing annuity contracts: financial risk and demographic risk. As regards the latter, recent work has focused on modelling the trend in mortality as a stochastic process. A popular method for modelling death rates is the Lee-Carter model. In this paper we gives an overview of the Lee Carter model and the feasibility of using it to construct mortality forecast for the population data. In particular, we focus on a sensitivity issue of this model and in order to deal with it, we illustrate the implementation of an experimental strategy to assess the robustness of the LC model. The next step, we experiment and apply it to a matrix of mortality rates. The results are applied to a pension annuity. There are investigating in particular the hypothesis about the error structure implicitly assumed in the model specification, after having assume that errors are homoscedastic. Analyzing the model it is estimated that the homoscedasticity assumption is quite unrealistic, because of the observed pattern of the mortality rates showing a different variability at different ages. Therefore, there is an emerging opportunity to analyze the strength of predictable parameter. The purpose of this study is a strategy in order to assess the strength of the Lee-Carter model inducing the errors to satisfy the homoscedasticity hypothesis. The impact of Lee Carter model on various financial calculations is the main focus of the paper. Furthermore, it is applied it to a matrix of mortality rates including a pension rate portfolio. The Albania model with the variables of death and birth is shown on this paper taken in consideration the Lee Carter Error.

scholarly journals The Heteroscedasticity Impact on Actuarial Science: Lee Carter Error Simulation

2018 ◽  
Vol 2 (1) ◽  
pp. 42
Author(s):  
Olgerta Idrizi ◽  
Besa Shahini
Keyword(s):  
Financial Risk ◽  
Population Data ◽  
Mortality Rates ◽  
Model Specification ◽  
Insurance Companies ◽  
Actuarial Science ◽  
Demographic Risk ◽  
The Impact ◽  
Error Simulation ◽  
Carter Model

C19 Life insurance companies deal with two fundamental types of risks when issuing annuity contracts: financial risk and demographic risk. As regards the latter, recent work has focused on modelling the trend in mortality as a stochastic process. A popular method for modelling death rates is the Lee-Carter model. In this paper we gives an overview of the Lee Carter model and the feasibility of using it to construct mortality forecast for the population data. In particular, we focus on a sensitivity issue of this model and in order to deal with it, we illustrate the implementation of an experimental strategy to assess the robustness of the LC model. The next step, we experiment and apply it to a matrix of mortality rates. The results are applied to a pension annuity. There are investigating in particular the hypothesis about the error structure implicitly assumed in the model specification, after having assume that errors are homoscedastic. Analyzing the model it is estimated that the homoscedasticity assumption is quite unrealistic, because of the observed pattern of the mortality rates showing a different variability at different ages. Therefore, there is an emerging opportunity to analyze the strength of predictable parameter. The purpose of this study is a strategy in order to assess the strength of the Lee-Carter model inducing the errors to satisfy the homoscedasticity hypothesis. The impact of Lee Carter model on various financial calculations is the main focus of the paper. Furthermore, it is applied it to a matrix of mortality rates including a pension rate portfolio. The Albania model with the variables of death and birth is shown on this paper taken in consideration the Lee Carter Error.

scholarly journals Forecasting Hungarian mortality rates using the Lee-Carter method

2007 ◽  
Vol 57 (1) ◽  
pp. 21-34 ◽  
Author(s):  
S. Baran ◽  
J. Gáll ◽  
M. Ispány ◽  
G. Pap
Keyword(s):  
Mortality Rates ◽  
Mortality Data ◽  
Good Prediction ◽  
Data Set ◽  
Men And Women ◽  
Carter Model

A modified version of the popular Lee-Carter method (Lee-Carter 1992) is applied to forecast mortality rates in Hungary for the period 2004–2040 on the basis of mortality data between 1949 and 2003 both for men and women. Another case is also considered based on a restricted data set corresponding to the period 1989–2003. The model fitted to the data of the period 1949–2003 forecasts increasing mortality rates for men between ages 45 and 55, pointing out that the Lee-Carter method is hardly applicable for countries where mortality rates exhibit trends as peculiar as in Hungary. However, models fitted to the data for the last 15 years both for men and women forecast decreasing trends similarly to the case of countries where the method was successfully applied. Hence one gets a better fit in this way, however, further concerns suggest that the Lee-Carter model, which is celebrated and widely used in actuarial practice, does not necessarily give sufficiently good prediction.

scholarly journals A Deep Learning Integrated Lee–Carter Model

Risks ◽  
2019 ◽  
Vol 7 (1) ◽  
pp. 33 ◽  
Author(s):  
Andrea Nigri ◽  
Susanna Levantesi ◽  
Mario Marino ◽  
Salvatore Scognamiglio ◽  
Francesca Perla
Keyword(s):  
Deep Learning ◽  
Short Term Memory ◽  
Predictive Accuracy ◽  
Mortality Rates ◽  
Short Term ◽  
Term Memory ◽  
The Future ◽  
Long Short Term Memory ◽  
Carter Model ◽  
Over Time

In the field of mortality, the Lee–Carter based approach can be considered the milestone to forecast mortality rates among stochastic models. We could define a “Lee–Carter model family” that embraces all developments of this model, including its first formulation (1992) that remains the benchmark for comparing the performance of future models. In the Lee–Carter model, the κ t parameter, describing the mortality trend over time, plays an important role about the future mortality behavior. The traditional ARIMA process usually used to model κ t shows evident limitations to describe the future mortality shape. Concerning forecasting phase, academics should approach a more plausible way in order to think a nonlinear shape of the projected mortality rates. Therefore, we propose an alternative approach the ARIMA processes based on a deep learning technique. More precisely, in order to catch the pattern of κ t series over time more accurately, we apply a Recurrent Neural Network with a Long Short-Term Memory architecture and integrate the Lee–Carter model to improve its predictive capacity. The proposed approach provides significant performance in terms of predictive accuracy and also allow for avoiding the time-chunks’ a priori selection. Indeed, it is a common practice among academics to delete the time in which the noise is overflowing or the data quality is insufficient. The strength of the Long Short-Term Memory network lies in its ability to treat this noise and adequately reproduce it into the forecasted trend, due to its own architecture enabling to take into account significant long-term patterns.

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