Lee–Carter mortality forecasting with age-specific enhancement

Renshaw, A. E.; Haberman, Steven

doi:10.1016/s0167-6687(03)00138-0

Cited by 344 publications

(294 citation statements)

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“…This assumption made also by Booth et al (2002) and by Renshaw and Haberman (2003b) represents a potencial weakness as Renshaw and Haberman (2003b) recognize. An example of how the model can be expanded to include dependence and co-integration effects is given in Renshaw and Haberman (2003c).…”

Section: Forecastingmentioning

confidence: 95%

“…It is for that reason that we apply this model to logit death probability q xt , Booth et al (2002) and Renshaw and Haberman (2003b) indicate that the interaction between age and time can be captured better by adding terms to (2), which would become…”

Section: Adjustment and Prediction Of Q Xtmentioning

confidence: 99%

“…with n number of ages, and s i , u i x and v i t the (ordered) singular values and respective left and right singular vectors (Renshaw and Haberman, 2003b).…”

Section: Lee-carter-svdmentioning

confidence: 99%

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Modelling and forecasting mortality in Spain

Debón

Montes

Puig

2008

European Journal of Operational Research

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Experience shows that static life tables overestimate death probabilities. As a consequence of this overestimation the premiums for annuities, pensions and life insurance are not what they actually should be, with negative effects for insurance companies or policy-holders. The reason for this overestimation is that static life tables, through being computed for a specific period of time, cannot take into account the decreasing mortality trend over time. Dynamic life tables overcome this problem by incorporating the influence of the calendar when graduating mortality. Recent papers on the topic look for the development of new methods to deal with this dynamism.Most methods used in dynamic tables are parametric, apply traditional mortality laws and then analyze the evolution of estimated parameters with time series techniques. Our contribution consists in extending and applying Lee-Carter methods to Spanish mortality data, exploring residuals and future trends.

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Section: Forecastingmentioning

confidence: 95%

Section: Adjustment and Prediction Of Q Xtmentioning

confidence: 99%

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Modelling and forecasting mortality in Spain

Debón

Montes

Puig

2008

European Journal of Operational Research

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“…As an adjunct to modelling, we smooth the fitted age modulating indices (0) (1), x x   , (using the S-plus super smoother) in order to avoid localised age induced anomalies when projecting mortality rates (Renshaw and Haberman (2003), Delwarde et al (2007)). The 6 sets of parameter patterns generated by the back-fitting exercise with lower truncation at age 60 are depicted in Fig 3. We particularly draw attention to the stability of these biennial patterns, 97(02)07, coupled with the near linearity of the period index t  .…”

Section: Apc Back-fittingmentioning

confidence: 99%

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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“…The Lee and Carter (1992)-model can easily be extended to include more time factors (in addition to κ t ) (see Renshaw and Haberman (2003a)). 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.…”

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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Lee–Carter mortality forecasting with age-specific enhancement

Cited by 344 publications

References 9 publications

Modelling and forecasting mortality in Spain

Modelling and forecasting mortality in Spain

On age-period-cohort parametric mortality rate projections

Longevity Risk

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