Forecasting age distribution of death counts: an application to annuity pricing

Shang, Han Lin; Haberman, Steven

doi:10.1017/s1748499519000101

Cited by 11 publications

(5 citation statements)

References 60 publications

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“…In terms of the key indices of interest for mortality forecasting, specially in an actuarial context, refs. [ 10 , 13 , 14 , 24 , 45 , 46 ] considered death rates, life expectancies and discounted annuity values. This paper evaluates if differences between three different extensions of the Lee-Carter model are reflected in the forecasts of different mortality indicators.…”

Section: Discussionmentioning

confidence: 99%

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

Debón

Haberman

Montes

et al. 2021

IJERPH

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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.

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Section: Discussionmentioning

confidence: 99%

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

Debón

Haberman

Montes

et al. 2021

IJERPH

Self Cite

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show abstract

“…All these transformations are better visualized from the age distribution of deaths ( ) than from the age-specific rates ( ). This explains why new models that fit the are emerging (Oeppen et al., 2008 ; Bergeron-Boucher et al., 2017 ; Mazzuco et al., 2018 ; Basellini & Camarda, 2019 ; Shang & Haberman, 2020 ). Moreover, mortality rates ( ), survival probabilities ( ) and the age distribution of deaths ( ) are complementary mathematical functions, and each one can be derived from the others (Heuveline et al., 2001 ).…”

Section: Datamentioning

confidence: 99%

What Can We Learn from the Functional Clustering of Mortality Data? An Application to the Human Mortality Database

Léger

Mazzuco

2021

Eur J Population

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This study analyzed whether there are different patterns of mortality decline among low-mortality countries by identifying the role played by all the mortality components. We implemented a cluster analysis using a functional data analysis (FDA) approach, which allowed us to consider age-specific mortality rather than summary measures, as it analyses curves rather than scalar data. Combined with a functional principal component analysis, it can identify what part of the curves is responsible for assigning one country to a specific cluster. FDA clustering was applied to the data from 32 countries in the Human Mortality Database from 1960 to 2018 to provide a comprehensive understanding of their patterns of mortality. The results show that the evolution of developed countries followed the same pattern of stages (with different timings): (1) a reduction of infant mortality, (2) an increase of premature mortality and (3) a shift and compression of deaths. Some countries were following this scheme and recovering the gap with precursors; others did not show signs of recovery. Eastern European countries were still at Stage (2), and it was not clear if and when they will enter Stage 3. All the country differences related to the different timings with which countries underwent the stages, as identified by the clusters.

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“…Modal age death corresponding to the maximum value of the density has become a better longevity indicator in low mortality population. ( Canudas-Romo 2008 [2] ,Canudas-Romo 2010 [3], Ouellette and Bourbeauet [4],Horiuchi et al 2013 [5] , Basellini and Camarda [6], Shang and Haberman [7] , Bergeron-Boucher et al [8]). Survival curves dimensions are used in mortality analysis to determine highest normal life duration that exceeds modal age, death around the modal age and the proportion of survivors in population (Cheung et al [9], Ebeling et al [10]).…”

Section: Introductionmentioning

confidence: 99%

Modelling Mortality in Kenya

Njenga,

Kipchirchir

2024

ARJOM

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This research work seeks to analysis the mortality trend experienced in Kenya over the sample period 1950 to 2021 using a multidimensional modeling framework. Life table functions, namely; life expectancy, survival function and age at death distribution are applied to depict mortality characteristics. Life expectancy and survival rate have significantly improved. There has been a shift in mortality status from a high mortality population, to an intermediate stage and mortality risk factors have increased across age. Mortality concentration curve and index within the Lorenz curve and Gini coefficient framework are used to analyze the lifespan inequality. Lifespan inequality is high with negligible improvements over time. Gompertz force of mortality is then estimated, which is statistically significant at 5% level. Deaths at exact age 25 is about 35 per ten thousand, with the rate death rate increasing by 6.09% per year starting from age 25. Under the assumptions of stable population, where the mortality and fertility functions are independent of time, Malthusian parameter is estimated which is less than zero for selected years. Kenya is a shrinking population and death rate decrease with increase in Malthusian parameter. Finally, to model long-term mortality rate forecast, Lee-Carter model is estimated. The model is statistically significant at 5% level explaining 78.4% of the variations. Expected life expectancy at a given age is projected to increase, with life expectancy at birth in 2030 and 2071 being 65.6 and 70.5 years respectively.

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Forecasting age distribution of death counts: an application to annuity pricing

Cited by 11 publications

References 60 publications

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

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

What Can We Learn from the Functional Clustering of Mortality Data? An Application to the Human Mortality Database

Modelling Mortality in Kenya

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