A new approximation of annuity prices for age-period-cohort models

This letter presents a new general formula for estimating annuity prices within a wide range of stochastic mortality models. The formula is constructed using two building blocks: an approximation technique based on the Wentzel-Kramers-Brillouin method for calculating the sum of correlated lognormal random variables, and an approximate expression for the moment generating function of the lognormal distribution. Notably, this formula is applicable to virtually all age-period-cohort models where period effects are represented by vector autoregressive models. This broad assumption encompasses the majority of existing stochastic mortality models in literature. Through a numerical illustration, we also demonstrate the reliability and precision of our new method in determining annuity prices.