Description: Recent trends in mortality suggest that future gains in life expectancy will occur after age 80. This fact stresses the need and the importance to obtain precise measures of mortality at the highest ages, which are always subject to uncertainty due to misreporting of age at death.

Description: We propose an age-shift model to modify the LC model and deal with the problem of parameters. The proposed method attains smaller estimation errors with respect to mean absolute percentage error or mean square error. We also apply the proposed age-shift model to the mortality rates of these four countries to evaluate the longevity risk in annuity products by measuring life expectancy.