Traditionally, actuaries have modeled mortality improvement using deterministic reduction factors, with little consideration of the associated uncertainty. As mortality improvement has become an increasingly significant source of financial risk, it has become important to measure the uncertainty in the forecasts. Probabilistic confidence intervals provided by the widely accepted Lee-Carter model are known to be excessively narrow, due primarily to the rigid structure of the model. In this paper, we relax the model structure by considering individual differences (heterogeneity) in each age-period cell. The proposed extension not only provides a better goodness-of-fit based on standard model selection criteria, but also ensures more conservative interval forecasts of central death rates and hence can better reflect the uncertainty entailed. We illustrate the results using US and Canadian mortality data.

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Mortality dynamics are subject to jumps that are due to events such as wars and pandemics. Such jumps can have a significant impact on prices of securities that are designed for hedging catastrophic mortality risk, and therefore should be taken into account in modeling. Although several singlepopulation mortality models with jump effects have been developed, they are not adequate for modeling trades in which the hedger's population is different from the population associated with the security being traded. In this article, we first develop a two-population mortality model with transitory jump effects, and then we use the proposed model and an economic-pricing framework to examine how mortality jumps may affect the supply and demand of mortality-linked securities.

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