Continuing increases in life expectancy beyond previously-held limits have brought to the fore the critical importance of mortality forecasting. Significant developments in mortality forecasting since 1980 are reviewed under three broad approaches: expectation, extrapolation and explanation. Expectation is not generally a good basis for mortality forecasting, as it is subjective; expert expectations are invariably conservative. Explanation is restricted to certain causes of death with known determinants. Decomposition by cause of death poses problems associated with the lack of independence among causes and data difficulties. Most developments have been in extrapolative forecasting, and make use of statistical methods rather than models developed primarily for age-specific graduation. Methods using two-factor models (age-period or age-cohort) have been most successful. The two-factor Lee–Carter method, and, in particular, its variants, have been successful in terms of accuracy, while recent advances have improved the estimation of forecast uncertainty. Regression-based (GLM) methods have been less successful, due to nonlinearities in time. Three-factor methods are more recent; the Lee–Carter age-period-cohort model appears promising. Specialised software has been developed and made available. Research needs include further comparative evaluations of methods in terms of the accuracy of the point forecast and its uncertainty, encompassing a wide range of mortality situations.

/pdf/mortality-modelling-and-forecasting-a-review-of-methods-57ywz2mf1x.pdf

Mortality modelling and forecasting: a review of methods

Demographic forecasting: 1980 to 2005 in review

Continuing increases in life expectancy beyond previously-held limits have brought to the fore the critical importance of mortality forecasting. Significant developments in mortality forecasting since 1980 are reviewed under three broad approaches: expectation, extrapolation and explanation. Expectation is not generally a good basis for mortality forecasting, as it is subjective; expert expectations are invariably conservative. Explanation is restricted to certain causes of death with known determinants. Decomposition by cause of death poses problems associated with the lack of independence among causes and data difficulties. Most developments have been in extrapolative forecasting, and make use of statistical methods rather than models developed primarily for age-specific graduation. Methods using two-factor models (age-period or age-cohort) have been most successful. The two-factor Lee^Carter method, and, in particular, its variants, have been successful in terms of accuracy, while recent advances have improved the estimation of forecast uncertainty. Regression-based (GLM) methods have been less successful, due to nonlinearities in time. Three-factor methods are more recent; the Lee^Carter age-periodcohort model appears promising. Specialised software has been developed and made available. Research needs include further comparative evaluations of methods in terms of the accuracy of the point forecast and its uncertainty, encompassing a wide range of mortality situations.

/pdf/mortality-modelling-and-forecasting-a-review-of-methods-by-h-59z7kwtdti.pdf

MORTALITY MODELLING AND FORECASTING: A REVIEW OF METHODS By H. Booth and L. Tickle

In 1825 British actuary Benjamin Gompertz made a simple but important observation that a law of geometrical progression pervades large portions of different tables of mortality for humans. The simple formula he derived describing the exponential rise in death rates between sexual maturity and old age is commonly referred to as the Gompertz equation—a formula that remains a valuable tool in demography and in other scientific disciplines. Gompertz’s observation of a mathematical regularity in the life table led him to believe in the presence of a law of mortality that explained why common age patterns of death exist. This law of mortality has captured the attention of scientists for the past 170 years because it was the first among what are now several reliable empirical tools for describing the dying-out process of many living organisms during a significant portion of their life spans. In this paper we review the literature on Gompertz’slaw of mortality and discuss the importance of his observations and insights in light of research on aging that has taken place since then.

Ever since gompertz

Annuities are contractual guarantees that promise to provide periodic income over the lifetime(s) of individuals. Standard insurance industry practice assumes independence of lives when valuing annuities where the promise is based on more than one life. This article investigates the use of dependent mortality models to value this type of annuity. We discuss a broad class of parametric models using a bivariate survivorship function called a copula. Using data from a large insurance company, we calculate maximum likelihood estimates to calibrate the model. The estimation results show strong positive dependence between joint lives with real economic significance. Annuity values are reduced by approximately 5 percent when dependent mortality models are used compared to the standard models that assume independence.

Annuity Valuation with Dependent Mortality

In this paper we study the underlying Gompertz distribution and develop formulae for the moments and other characteristics of this useful but apparently unknown distribution. We find that the skewness and kurtosis of the distribution are fixed constants independent of the two distribution parameters and this would appear to be the reason for the mixed success writers have experienced fitting the curve to fertility data. We also show the distribution of the minimum of n independent Gompertz variables all having the same c-parameter is itself a Gompertz variable with the same c-parameter. (SUMMARY IN FRE AND ITA) (EXCERPT)

Emil J. Valkovics

Papers

The Gompertz distribution and its applications.