Variations of the linear logarithm hazard transform for modelling cohort mortality rates

Observing that there is a linear relationship between two sequences of the logarithm of the forces of mortality (hazard rates of the future lifetime) for two years, two variations of the linear logarithm hazard transform (LLHT) model are proposed in this project. We first regress the sequence of the logarithm of the forces of mortality for a cohort in year y on that for a base year. Next, we repeat the same procedure a number of times with y increased by one and the base year unchanged each time, and produce two sequences of slope and intercept parameters which both look linear. Then the simple linear regression and random walk with drift model are applied to each of these two parameter sequences. The fitted parameters can be used to forecast cohort mortality rates. Deterministically and stochastically forecasted cohort mortality rates with the two LLHT-based approaches, and the Lee-Carter and CBD models are presented, and their corresponding forecasted errors and associated confidence intervals are calculated for comparing the forecasting performances. Applications in pricing term life insurance and annuities are also given for illustration.