Retrospective reserves for the insurances of the person in the framework of multistate models

Retrospective reserve is usually meant as the expected accumulated value at a given time of past premiums less benefits. With reference to multistate models, both the state of the policy at the time of velitation and its past story must be considered in calculating such expected value. Since it is unlikely that the retrospective reserve can be evaluated for any possible path of the risk, different definitions can be given according to the hypotheses on its story. In this paper we firstly examine the main definitions of retrospective reserve given in the framework of multistate models. Then, we formative a new definition which generalizes that given in conventional life insurance mathematics. Comparisons among the various definitions are proposed in some exmple which, inter alias, show the different behaviour and magnitude of such reserves.