Age-coherent extensions of the Lee–Carter model

Gao, Guangyuan; Shi, Yanlin

doi:10.1080/03461238.2021.1918578

Cited by 10 publications

(15 citation statements)

References 33 publications

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“…Li et al (2013) achieve rotation by letting the b x 's from the original model converge (smoothly) to some assumed long-term target B x . The approach has since been adopted and adapted by a number of authors, for example Vékás (2019) and Gao and Shi (2021).…”

Section: Alternative Ways Of Addressing Changing Improvement Ratesmentioning

confidence: 99%

The Saint Model: A Decade Later

Jarner¹,

Jallbjørn²

2022

ASTIN Bull.

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While many of the prevalent stochastic mortality models provide adequate short- to medium-term forecasts, only few provide biologically plausible descriptions of mortality on longer horizons and are sufficiently stable to be of practical use in smaller populations. Among the very first to address the issue of modelling adult mortality in small populations was the SAINT model, which has been used for pricing, reserving and longevity risk management by the Danish Labour Market Supplementary Pension Fund (ATP) for more than a decade. The lessons learned have broadened our understanding of desirable model properties from the practitioner’s point of view and have led to a revision of model components to address accuracy, stability, flexibility, explainability and credibility concerns. This paper serves as an update to the original version published 10 years ago and presents the SAINT model with its modifications and the rationale behind them. The main improvement is the generalization of frailty models from deterministic structures to a flexible class of stochastic models. We show by example how the SAINT framework is used for modelling mortality at ATP and make comparisons to the Lee-Carter model.

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Section: Alternative Ways Of Addressing Changing Improvement Ratesmentioning

confidence: 99%

The Saint Model: A Decade Later

Jarner¹,

Jallbjørn²

2022

ASTIN Bull.

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“…Intuitively, age coherence means that predicted mortality rates (of the same population) across ages should not differ indefinitely. Consistent with Li and Lu (2017), Gao and Shi (2021) and Li and Shi (2021), we formally define age coherence as follows.…”

Section: Coherent Mortality Modelsmentioning

confidence: 99%

“…Other than working with the VAR framework, a recent study by Gao and Shi (2021) proposes two effective age-coherent extensions of the LC model. Both are motivated by Li et al (2013) to rotate bx,h gradually over time.…”

Section: Age-coherent Extensions Of the Lc Modelmentioning

confidence: 99%

“…The rotation is supported by the fact that mortality decline decelerates at younger ages and accelerates at old ages (Li et al, 2013). Also, to realize age coherence in the long run, Gao and Shi (2021) require that bx,h eventually converge (rotate) to a constant 1/N for all ages (a flat line). The rationale of 1/N comes from the constraint that Specifically, the first extension adopts the autoregressive (AR) framework.…”

Section: Age-coherent Extensions Of the Lc Modelmentioning

confidence: 99%

“…The desirable age coherence is realized by its established cointegration feature. Another novel attempt is the age-coherent extensions of the LC model using the hyperbolic (LC-H) and geometric (LC-G) convergences in the relative speeds of age-specific mortality decline (Gao and Shi, 2021). A similar principal is adopted to the sparse VAR (SVAR) model by Li and Shi (2021), and we name the SVAR model using hyperbolic and geometric convergences in the long-term mean by SVAR-H and SVAR-G, respectively.…”

Section: Introductionmentioning

confidence: 99%

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Forecasting mortality rates with a coherent ensemble averaging approach

Chang

Shi

2022

ASTIN Bull.

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Modeling and forecasting of mortality rates are closely related to a wide range of actuarial practices, such as the designing of pension schemes. To improve the forecasting accuracy, age coherence is incorporated in many recent mortality models, which suggests that the long-term forecasts will not diverge infinitely among age groups. Despite their usefulness, misspecification is likely to occur for individual mortality models when applied in empirical studies. The reliableness and accuracy of forecast rates are therefore negatively affected. In this study, an ensemble averaging or model averaging (MA) approach is proposed, which adopts age-specific weights and asymptotically achieves age coherence in mortality forecasting. The ensemble space contains both newly developed age-coherent and classic age-incoherent models to achieve the diversity. To realize the asymptotic age coherence, consider parameter errors, and avoid overfitting, the proposed method minimizes the variance of out-of-sample forecasting errors, with a uniquely designed coherent penalty and smoothness penalty. Our empirical data set include ten European countries with mortality rates of 0–100 age groups and spanning 1950–2016. The outstanding performance of MA is presented using the empirical sample for mortality forecasting. This finding robustly holds in a range of sensitivity analyses. A case study based on the Italian population is finally conducted to demonstrate the improved forecasting efficiency of MA and the validity of the proposed estimation of weights, as well as its usefulness in actuarial applications such as the annuity pricing.

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