Stochastic Period and Cohort Effect State-Space Mortality Models Incorporating Demographic Factors via Probabilistic Robust Principal Components

Toczydlowska, Dorota; Peters, Gareth W.; Fung, Man Chung; Shevchenko, Pavel V.

doi:10.3390/risks5030042

Cited by 10 publications

(3 citation statements)

References 40 publications

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“…Fung et al, (2019) further improved these mortality models by incorporating cohort features under the state-space framework and these mortality models with cohort effects can be formulated, estimated and forecasted under a Bayesian state-space framework. Toczydlowska et al, (2017) developed the family of LC stochastic mortality models by including exogenous observable demographic features that can be adopted to improve model fit and enhance forecast accuracy.…”

Section: Background On Univariate Mortality Modellingmentioning

confidence: 99%

Mortality models incorporating long memory for life table estimation: a comprehensive analysis

2021

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Mortality projection and forecasting of life expectancy are two important aspects of the study of demography and life insurance modelling. We demonstrate in this work the existence of long memory in mortality data. Furthermore, models incorporating long memory structure provide a new approach to enhance mortality forecasts in terms of accuracy and reliability, which can improve the understanding of mortality. Novel mortality models are developed by extending the Lee–Carter (LC) model for death counts to incorporate a long memory time series structure. To link our extensions to existing actuarial work, we detail the relationship between the classical models of death counts developed under a Generalised Linear Model (GLM) formulation and the extensions we propose that are developed under an extension to the GLM framework known in time series literature as the Generalised Linear Autoregressive Moving Average (GLARMA) regression models. Bayesian inference is applied to estimate the model parameters. The Deviance Information Criterion (DIC) is evaluated to select between different LC model extensions of our proposed models in terms of both in-sample fits and out-of-sample forecasts performance. Furthermore, we compare our new models against existing models structures proposed in the literature when applied to the analysis of death count data sets from 16 countries divided according to genders and age groups. Estimates of mortality rates are applied to calculate life expectancies when constructing life tables. By comparing different life expectancy estimates, results show the LC model without the long memory component may provide underestimates of life expectancy, while the long memory model structure extensions reduce this effect. In summary, it is valuable to investigate how the long memory feature in mortality influences life expectancies in the construction of life tables.

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Section: Background On Univariate Mortality Modellingmentioning

confidence: 99%

Mortality models incorporating long memory for life table estimation: a comprehensive analysis

2021

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“…Consequently, they suggested improving the estimates by smoothing β x independently from the other parameters. Furthermore, in order to improve model fit and forecast, Toczydlowska et al (2017) introduced exogenous observable demographic features into the family of LC stochastic mortality models.…”

Section: Motivation and Backgroundmentioning

confidence: 99%

Multivariate Long-Memory Cohort Mortality Models

2019

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The existence of long memory in mortality data improves the understandings of features of mortality data and provides a new approach for establishing mortality models. The findings of long-memory phenomena in mortality data motivate us to develop new mortality models by extending the Lee–Carter (LC) model to death counts and incorporating long-memory model structure. Furthermore, there are no identification issues arising in the proposed model class. Hence, the constraints which cause many computational issues in LC models are removed. The models are applied to analyse mortality death count data sets from three different countries divided according to genders. Bayesian inference with various selection criteria is applied to perform the model parameter estimation and mortality rate forecasting. Results show that multivariate long-memory mortality model with long-memory cohort effect model outperforms multivariate extended LC cohort model in both in-sample fitting and out-sample forecast. Increasing the accuracy of forecasting of mortality rates and improving the projection of life expectancy is an important consideration for insurance companies and governments since misleading predictions may result in insufficient funds for retirement and pension plans.

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“…The arguably most well-received modern mortality model is the Lee and Carter (1992) model and its extensions using time series analysis. For instance, it has been generalized to multivariate populations with a common trend (Li and Lee, 2005), mortality forecasts using single value decomposition (Renshaw and Haberman, 2003), joint modeling of different national populations (Antonio et al, 2015) and sub-populations (Villegas and Haberman, 2014), a multi-population stochastic mortality model (Danesi et al, 2015), a Poisson regression model (Brouhns et al, 2002), and stochastic period and cohort effect (Toczydlowska et al, 2017), among others. A key advantage of the Lee-Carter model and its invariant is that statistical inferences from time series analysis can be applied or generalized to estimate and test with a real mortality data set.…”

Section: Introductionmentioning

confidence: 99%

Volterra mortality model: Actuarial valuation and risk management with long-range dependence

Chiu

Wong

2020

Preprint

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While abundant empirical studies support the long-range dependence (LRD) of mortality rates, the corresponding impact on mortality securities are largely unknown due to the lack of appropriate tractable models for valuation and risk management purposes. We propose a novel class of Volterra mortality models that incorporate LRD into the actuarial valuation, retain tractability, and are consistent with the existing continuous-time affine mortality models. We derive the survival probability in closed-form solution by taking into account of the historical health records. The flexibility and tractability of the models make them useful in valuing mortality-related products such as death benefits, annuities, longevity bonds, and many others, as well as offering optimal mean-variance mortality hedging rules. Numerical studies are conducted to examine the effect of incorporating LRD into mortality rates on various insurance products and hedging efficiency.

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Stochastic Period and Cohort Effect State-Space Mortality Models Incorporating Demographic Factors via Probabilistic Robust Principal Components

Cited by 10 publications

References 40 publications

Mortality models incorporating long memory for life table estimation: a comprehensive analysis

Mortality models incorporating long memory for life table estimation: a comprehensive analysis

Multivariate Long-Memory Cohort Mortality Models

Volterra mortality model: Actuarial valuation and risk management with long-range dependence

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