A Quantitative Comparison of Stochastic Mortality Models Using Data from England &amp; Wales and the United States

Cairns, Andrew J. G.; Blake, David; Dowd, Kevin; Coughlan, Guy; Epstein, David

doi:10.2139/ssrn.1340389

Cited by 163 publications

(359 citation statements)

References 17 publications

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“…Faced with the need (in our judgement), to preserve this representation in order to ensure the capture of age effects in a complex modelling situation, we have chosen to adapt the original Lee-Carter (1992) two-stage fitting strategy when fitting APC, by conditioning on a predetermined static life table in order to represent the main ageeffects. We see no reason to change this approach to fitting APC by incorporating iterative adjustments to the main age effects, as suggested by Cairns et al (2009), especially given the wider objective of model projection. In our limited experience of incorporating the Cairns et al (2009) suggestion into the iterative fitting algorithm, we have observed that the already slow rate of convergence is made appreciably slower, and so, we believe that it should be avoided on purely practical grounds.…”

Section: Data Arraymentioning

confidence: 99%

“…We see no reason to change this approach to fitting APC by incorporating iterative adjustments to the main age effects, as suggested by Cairns et al (2009), especially given the wider objective of model projection. In our limited experience of incorporating the Cairns et al (2009) suggestion into the iterative fitting algorithm, we have observed that the already slow rate of convergence is made appreciably slower, and so, we believe that it should be avoided on purely practical grounds. The question as to whether the iterative fitting process then results in attainment of a global optimisation has still to be resolved.…”

Section: Data Arraymentioning

confidence: 99%

“…Concerning the use of extrapolated mortality rates in the valuation of fixed rate annuities at typical retirement ages, the question of data truncation by age, prior to modelling, may need to be considered (Cairns et al (2009) As illustrated, these require the retention of (a) data aged 60 and above, and (b) data aged 43 and above, allowing for the allocation of zero weights in the last c = 5 cohort years (say). Clearly, data below these age limits contribute directly to the relevant cohort years under ageperiod-cohort modelling.…”

Section: Data Truncationmentioning

confidence: 99%

See 2 more Smart Citations

On age-period-cohort parametric mortality rate projections

Haberman

Renshaw

2009

Insurance: Mathematics and Economics

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This is the accepted version of the paper.This version of the publication may differ from the final published version. Abstract: An augmented version of the Lee-Carter modelling approach to mortality forecasting, extended to include an age modulated cohort index in addition to the standard age modulated period index is described and tested for prediction robustness. Life expectancy and annuity value predictions, at pensioner ages and various periods are compared, both with and without the age modulated cohort index, for the England & Wales male mortality experience. The simulation of prediction intervals for these indices of interest is discussed in detail. Permanent repository link(i) H0: log{mu(x,t)} = alpha(x) + kappa(t) + iota(t-x)(ii) H0: log{mu(x,t)} = alpha(x) + iota(t-x) + kappa(t) (iii) H0: log{mu(x,t)} = kappa(t) + iota(t-x) + alpha(x) England & Wales 1961 male mortality experience, ages 0-99. Linear structure H0: comprising main age-period-cohort effects fitted in different orders, as specified in the above captions. Main age effect (1st column), main period effect (2nd column), main cohort effect (3rd column). Single stage fitting process, with different model formulae. Reduction factor parameter patterns, with beta parameter smoothing. beta vs age period 1961-1997 1965 1970 1975 1980 1985 1990 1995 beta vs age period 1961-1999 1965 1970 1975 1980 1985 1990 1995 1965 1970 1975 1980 1985 1990 1995 -of-birth: 1902, 1910, 1918, 1926, 1934, 1942. 4% annuity a(x,t) 1965 1970 1975 1980 1985 1990 1995 Evolving biennial (1997, 99, 01, 03, 05, 2007) life expectancy and 4% fixed rate annuity predictions, by cohort trajectory: presented in decreasing sequence, for individuals aged 65, 70, 75, 80 respectively.Fig 1.Prediction intervals by bootstrapping the time series prediction error and selecting 2.5, 50, 97.5 percentiles. 4% annuity a(x,t) Evolving biennial (1997, 99, 01, 03, 05, 2007) life expectancy and 4% fixed rate annuity predictions, by cohort trajectory: presented in decreasing sequence, for individuals aged 65, 70, 75, 80 respectively. Prediction intervals by simulation and selecting 2.5, 50, 97.5 percentiles using Algorithm 1 and Algorithm 2, with and without allowance for time series parameter error (pe). 4% annuity a(x,t) 1On age-period-cohort parametric mortality rate projections. AbstractAn augmented version of the Lee-Carter modelling approach to mortality forecasting, extended to include an age modulated cohort index in addition to the standard age modulated period index is described and tested for prediction robustness. Life expectancy and annuity value predictions, at pensioner ages and various periods are compared, both with and without the age modulated cohort index, for the England & Wales male mortality experience. The simulation of prediction intervals for these indices of interest is discussed in detail.

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Section: Data Arraymentioning

confidence: 99%

Section: Data Arraymentioning

confidence: 99%

Section: Data Truncationmentioning

confidence: 99%

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On age-period-cohort parametric mortality rate projections

Haberman

Renshaw

2009

Insurance: Mathematics and Economics

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“…Currie et al (2004) propose a model assuming smoothness across both ages and years. Cairns et al (2007Cairns et al ( , 2008b provide an extensive comparison of these various time series based stochastic mortality models.…”

Section: Recent Dynamic Mortality Modelsmentioning

confidence: 99%

“…This means that we include process and parameter risk in the future death probabilities on the basis of the Lee and Carter (1992)-approach. In addition, we shall allow for uncertainty in the model-variant choice: We include next to the traditional Lee and Carter (1992)-model also the variants proposed by Brouhns et al (2002a) and Cairns et al (2007). In this way we also allow for model risk.…”

Section: Discounted Present Value Of Liabilitiesmentioning

confidence: 99%

Longevity Risk

2010

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SummaryMost of the western world has seen a steady increase in the average lifetime of its inhabitants over the past century. Although the past trends suggest that further changes in mortality rates are to be expected, considerable uncertainty exists regarding the future development of mortality. This type of uncertainty is referred to as longevity risk. This paper reviews the current state of the literature concerning longevity risk. First, we discuss the modeling of future mortality, including the Lee and Carter (J Am Stat Assoc 87:659-671, 1992)-approach, as well as other approaches. Second, we discuss the importance of longevity risk for the solvency of portfolios of pension and life insurance products. Finally, we investigate possibilities for longevity risk management. In particular, we consider longevity risk management through securitization and/or pension and insurance (re)design.

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Identifying subgroups of age and cohort effects in obesity prevalence

Miljkovic

Wang

2020

Biometrical J

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The obesity epidemic represents an important public health issue in the United States. Studying obesity trends across age groups over time helps to identify crucial relationships between the disease and medical treatment allowing for the development of effective prevention policies. We aim to define subgroups of age and cohort effects in obesity prevalence over time by considering an optimization approach applied to the age‐period‐cohort (APC) model. We consider a heterogeneous regression problem where the regression coefficients are age dependent and belong to subgroups with unknown grouping information. Using the APC model, we apply the alternating direction method of multipliers (ADMM) algorithm to develop a two‐step algorithm for (1) subgrouping of cohort effects based on similar characteristics and (2) subgrouping age effects over time. The proposed clustering approach is illustrated for the United States population, aged 18–79, during the period 1990–2017.

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A Quantitative Comparison of Stochastic Mortality Models Using Data from England & Wales and the United States

Cited by 163 publications

References 17 publications

On age-period-cohort parametric mortality rate projections

On age-period-cohort parametric mortality rate projections

Longevity Risk

Identifying subgroups of age and cohort effects in obesity prevalence

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