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Modeling longevity risks using a principal component approach: a comparison with existing stochastic mortality models. (English) Zbl 1231.91254

Summary: This research proposes a mortality model with an age shift to project future mortality using principal component analysis (PCA). Comparisons of the proposed PCA model with the well-known models – the Lee-Carter model, the age-period-cohort model, and the Cairns, Blake, and Dowd model – employ empirical studies of mortality data from six countries, two each from Asia, Europe, and North America. The mortality data come from the human mortality database and span the period 1970–2005. The proposed PCA model produces smaller prediction errors for almost all illustrated countries in its mean absolute percentage error. To demonstrate longevity risk in annuity pricing, we use the proposed PCA model to project future mortality rates and analyze the underestimated ratio of annuity price for whole life annuity and deferred whole life annuity product respectively. The effect of model risk on annuity pricing is also investigated by comparing the results from the proposed PCA model with those from the LC model. The findings can benefit actuaries in their efforts to deal with longevity risk in pricing and valuation.

MSC:

91B30 Risk theory, insurance (MSC2010)
91B70 Stochastic models in economics
62H25 Factor analysis and principal components; correspondence analysis
62P05 Applications of statistics to actuarial sciences and financial mathematics
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