A cohort-based extension to the Lee–Carter model for mortality reduction factors

Renshaw, A. E.; Haberman, Steven

doi:10.1016/j.insmatheco.2005.12.001

Cited by 577 publications

(618 citation statements)

References 12 publications

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“…This resolution involves the simulation of the forecast error in the associated ( ,1, ) ARIMA p q applied to the main period effect, while ignoring the model fitting error: this latter component is found to be of negligible effect in comparison, a result which is in general agreement with the original findings of Lee and Carter (1992). The simulation strategy that we adopt reads as follows Renshaw and Haberman (2006): data in the age range 90-99 are no longer readily available from the GAD website.…”

Section: Prediction Intervalssupporting

confidence: 59%

“…Denote a rectangular mortality data array   Renshaw and Haberman (2006), using just three of the many different model formulae possible (design matrices): corresponding to the order in which the three ageperiod-cohort main effects are specified in the individual captions. This generates three different sets of parameter patterns: only for x  are the patterns stable and they provide a realistic representation of the main age effects which match the typical shape of a static life table on the log scale.…”

Section: Data Arraymentioning

confidence: 99%

“…Here, we have highlighted the decomposition of the forecast mortality rates into the product of a static life table   exp x  and mortality reduction (adjustment) factor F. In this approach, we ensure 'continuity' with the latest estimated mortality rates, as opposed to the latest observed mortality rates (as in Renshaw and Haberman (2006)), in the transition to the extrapolated mortality rates. We believe that this feature has a minimal effect on the indices of interest which are computed subsequently (Section 2.8) and hence it is applied consistently throughout this paper.…”

Section: Model Dynamicsmentioning

confidence: 99%

“…In Renshaw and Haberman (2006), a method of incorporating cohort effects into the parametric structure of the basic Lee-Carter (LC) model for mortality projection was introduced and illustrated (through an age-period-cohort model, abbreviated here to APC). In this sequel, we investigate certain wider aspects of this approach to mortality rate projection.…”

Section: Introductionmentioning

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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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: Prediction Intervalssupporting

confidence: 59%

Section: Data Arraymentioning

confidence: 99%

Section: Model Dynamicsmentioning

confidence: 99%

Section: Introductionmentioning

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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“…However, Tuljapurkar et al (2000), investigating the G7 countries (Canada, France, Germany, Italy, Japan, UK, and US), 16 find that a single factor (as in the original Lee and Carter (1992) specification) already suffices to explain over 94% of the variance in the log-specific raw central death rates. Nevertheless, to improve the forecast performance, it might be better to include an additional cohort-specific factor (see Renshaw and Haberman 2006).…”

Section: The Lee and Carter Approachmentioning

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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Longevity Risk and Life Annuities

Milevsky

2008

Encyclopedia of Quantitative Risk Analysis and Assessment

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Longevity risk is faced by individuals, corporations, as well as society and their governments. This brief article reviews the various dimensions and aspects of longevity risk as they relate to the market for life annuities and mortality‐contingent claims. The main argument used is that regardless of one's perspective on longevity risk, this field will continue to provide fertile ground for advanced research for many, albeit uncertain, years to come.

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A cohort-based extension to the Lee–Carter model for mortality reduction factors

Cited by 577 publications

References 12 publications

On age-period-cohort parametric mortality rate projections

On age-period-cohort parametric mortality rate projections

Longevity Risk

Longevity Risk and Life Annuities

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