A Markov process interest and mortality model

For several years stochastic models have been proposed that are able to capture uncertainty linked to the future development both of \ufb01nancial and demographic components inherent in the policy. We consider a multistate life insurance contract and propose a model where both the interest intensity and the transition intensities, the latter describing the demographic structure, are managed by multistate stochastic models. In particular, we study a life insurance contract and derive di\ufb00erential equations of the mathematical prospective reserve. Finally, we study mean values of actualization factors and survival probabilities, and derive the di\ufb00erential equations they satisfy. Such results allow us to obtain adequate premium \ufb02ows. Mathematics Sub ject Classi\ufb01cations (2000). 60J27, 91B30, 91B7