A note on stochastic survival probabilities and their calibration

In this note we use doubly stochastic processes (or Cox processes) in order to model the evolution of the stochastic force of mortality of an individual aged x. These processes have been widely used in the credit risk literature in modelling the default arrival, and in this context have proved to be quite flexible and useful. We investigate the applicability of these processes in describing the individual's mortality, and provide a calibration to the Italian case. Results from the calibration are twofold. Firstly, the stochastic intensities seem to better capture the development of medicine and long term care which is under our daily observation. Secondly, when pricing insurance products such as life annuities, we observe a remarkable premium increase, although the expected residual lifetime is essentially unchanged.