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.

Description: When people retire, purchasing the annuity insurances using their retirement fund is one way against the longevity risk. However, it has some shortcoming- the annual payment may be insufficient for daily life consumption and can’t be adjusted for any urgent need [liquidity risk]. This is the abstract of a paper that investigates the adequate annuitization timing and optimal asset allocation under different investment strategies that can be found according to a time-series of safety level as a utility function for a retiree.