Mortality crossover

(Feb 24, 2020)

In a previous blog I discussed the importance of mortality convergence to actuaries, i.e. how mortality differentials narrow with age and how this interacts with discounting of cashflows. The traditional approach to allowing for mortality convergence is to have two parameters, one for the main effect of a risk factor and a second to allow the impact to vary by age. This second parameter is known as an interaction. However, one unwelcome side-effect of this is mortality crossover, an example of which is shown in Figure 1:

Figure 1. Gompertz model by age and pension size, showing mortality convergence but also crossover between ages 85 and 90.  Source: Macdonald et al (2018).

As pointed out in Richards (2019),

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Tags: mortality convergence, crossover

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