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Modeling mortality with a Bayesian vector autoregression. (English) Zbl 1452.91244

Summary: Parametric mortality models capture the cross section of mortality rates. These models fit the older ages better, because of the more complex cross section of mortality at younger and middle ages. Dynamic parametric mortality models fit a time series to the parameters, such as a vector autoregression (VAR), in order to capture trends and uncertainty in mortality improvements. We consider the full age range using the Heligman and Pollard model [L. Heligman and J. H. Pollard, “The age pattern of mortality”, J. Inst. Actuar. 107, No. 1, 49–80 (1980; doi:10.1017/S0020268100040257)], a cross-sectional mortality model with parameters that capture specific features of different age ranges. We make the Heligman-Pollard model dynamic using a Bayesian vector autoregressive (BVAR) model for the parameters and compare with more commonly used VAR models. We fit the models using Australian data, a country with similar mortality experience to many developed countries. We show how the BVAR models improve forecast accuracy compared to VAR models and quantify parameter risk which is shown to be significant.

MSC:

91D20 Mathematical geography and demography
91G05 Actuarial mathematics
62P05 Applications of statistics to actuarial sciences and financial mathematics
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