Non mean reverting affne processes for stochastic mortality
In this paper we use doubly stochastic processes (or Cox processes) in order to model the random evolution of mortality of an individual. These processes have been widely used in the credit risk literature in modelling default arrival, and in this context have proved to be quite flexible, especially when the intensity process is of the affne class. We investigate the applicability of time-homogeneous a±ne processes in describing the individual's intensity of mortality and the mortality trend, as well as in forecasting it. We calibrate them to the UK population. Calibrations suggest that, in spite of their popularity in the financial context, mean reverting time-homogeneous processes are less suitable for describing the death intensity of individuals than non mean reverting processes. Among the latter, affne processes whose determin- istic part increases exponentially seem to be appropriate. They are natural generalizations of the Gompertz law. Stress analysis and analytical results indicate that increasing the randomness of the intensity process for a given cohort results in improvements in survivorship. Mortality forecasts and their comparison with experienced mortality rates provide further encour- aging evidence in favour of non mean reverting processes. The mortality trend is evidenced through the evolution over time of the parameters and through the intensity simulation for di®erent gener- ations.
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