APC模型.pdfVIP

Insurance: Mathematics and Economics 38 (2006) 556–570 A cohort-based extension to the Lee–Carter model for mortality reduction factors A.E. Renshaw, S. Haberman ∗ Cass Business School, City University, London, EC1Y 8TZ, UK Received September 2005; received in revised form December 2005; accepted 9 December 2005 Abstract The Lee–Carter modelling framework is extended through the introduction of a wider class of generalised, parametric, non-linear models. This permits the modelling and extrapolation of age-specific cohort effects as well as the more familiar age-specific period effects. The choice of error distribution is generalised. © 2005 Elsevier B.V. All rights reserved. Keywords: Cohort effects; Mortality reduction factors; Generalised non-linear models; Time series; Mortality projections 1. Introduction The projection of mortality trends is an important issue in a wide number of areas: for example, planning for social security and health care systems and for the funding of retirement income systems and, in actuarial applications, for the pricing and reserving of annuity portfolios. The Lee–Carter methodology has proved to be an elegant and effective method of forecasting demographic variables including mortality (Lee and Carter, 1992), which are gaining wide acceptance: for example, it is used as a benchmark methodology by the US Bureau of the Census. Mortality reduction factors (CMI, 1999) are seen as an important means of capturing and projecting historic mortality trends (Renshaw and Haberman, 2003b). They are central to the extrapolation of mortality trends using the Lee–Carter methodology (Lee, 2000) and its Poisson based equivalent (Brouhns et al., 2002a). These methods, as originally constituted, con