An additive stochastic model of mortality rates: An application to longevity risk in reserve evaluation
The paper proposes an additive continuous-time stochastic mortality model which revises that (B&H model) of Ballotta and Haberman (2006). The structure of the B&H model implies that the future hazard rate is proportional to the stochastic component, thus inducing two questionable features. First, in the B&H model, the uncertainty of the future hazard rate will be enlarged as the base hazard rate increases. However, an increase in the base hazard rate may not cause a dramatic increase suggested by the exponential component of B&H (2006). Second, in the B&H model, the uncertainty of the future hazard rate will be larger in the group which is older and will be greatly augmented by the interaction of age and time. But the uncertainty of the future hazard rate may not increase with an increase in age. The problems can be resolved by our additive structure which is the sum of a deterministic estimator and a stochastic component. Since using the additive structure will contribute to the fact that the stochastic component is independent of age and the base hazard rate, in our model the uncertainty of the future hazard rate will not be affected by an increase in age or in the base hazard rate. We further demonstrate an application of our model by calculating reserves of longevity risks for pure endowments and various common annuity products in the UK. We also compare our results with those of the B&H model.
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