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Smoothing Poisson common factor model for projecting mortality jointly for both sexes. (English) Zbl 1390.91204

Summary: We consider a modification to the Poisson common factor model and utilise a generalised linear model (GLM) framework that incorporates a smoothing process and a set of linear constraints. We extend the standard GLM model structure to adopt Lagrange methods and \(P\)-splines such that smoothing and constraints are applied simultaneously as the parameters are estimated. Our results on Australian, Canadian and Norwegian data show that this modification results in an improvement in mortality projection in terms of producing more accurate forecasts in the out-of-sample testing. At the same time, projected male-to-female ratio of death rates at each age converges to a constant and the residuals of the models are sufficiently random, indicating that the use of smoothing does not adversely affect the fit of the model. Further, the irregular patterns in the estimates of the age-specific parameters are moderated as a result of smoothing and this model can be used to produce more regular projected life tables for pricing purposes.

MSC:

91B30 Risk theory, insurance (MSC2010)
62P05 Applications of statistics to actuarial sciences and financial mathematics
91D20 Mathematical geography and demography

Software:

gamair
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References:

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