A Poisson log-bilinear regression approach to the construction of projected lifetables

Abstract

General rightsCopyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights.-Users may download and print one copy of any publication from the public portal for the purpose of private study or research -You may not further distribute the material or use it for any profit-making activity or commercial gain -You may freely distribute the URL identifying the publication in the public portal Take down policy If you believe that this document breaches copyright, please contact us providing details, and we will remove access to the work immediately and investigate your claim. (2000) 91] recommendation for improving the Lee-Carter approach to the forecasting of demographic components. Specifically, the original method is embedded in a Poisson regression model, which is perfectly suited for age-sex-specific mortality rates. This model is fitted for each sex to a set of age-specific Belgian death rates. A time-varying index of mortality is forecasted in an ARIMA framework. These forecasts are used to generate projected age-specific mortality rates, life expectancies and life annuities net single premiums. Finally, a Brass-type relational model is proposed to adapt the projections to the annuitants population, allowing for estimating the cost of adverse selection in the Belgian whole life annuity market.

Epidemics in Ming and Qing China: Impacts of changes of climate and economic well-being

“…Thus, the ARX model will be further implemented with Poisson regression, which is the most suitable method for treating and validating count data (Cameron and Trivedi, 1998). A Poisson regression is designed in a format of logarithm model (Brouhns et al, 2002). A PoissoneARX model is established based on the ARX results.…”

Longevity Risk

“…Therefore, a Poisson process might be a more plausible way to model the number of deaths. Brouhns et al (2002a) model the integer-valued number of deaths D x,t as a Poisson distributed random variable,…”

“…The systematic part of the central death rate (or force of mortality) is again modeled in line with Lee and Carter (1992) as m x,t = exp (α x + β x κ t ). This model can be estimated like the Brouhns et al (2002a)-model, and the longevity risk can be quantified by means of bootstrapping. The Lee and Carter (1992)-model implicitly assumes that there is no heterogeneity in the measurement error terms x,t , see (14).…”

“…The Lee and Carter (1992)-model implicitly assumes that there is no heterogeneity in the measurement error terms x,t , see (14). Li et al (2006) propose a way to incorporate heterogeneity into the Brouhns et al (2002a)variant of the Lee and Carter (1992)-model. Alternatively, suggest to use the Negative Binomial distribution to allow for more heterogeneity.…”

“…Renshaw and Haberman (2003b) propose to first estimate the parameters of the model using the one-year age groups and then to smooth using, for instance, a cubic spline. More recently, propose to smooth the β x parameters as part of the first step, using a penalized log-likelihood approach in the Brouhns et al (2002a)-variant of the Lee and Carter (1992)-model.…”