  The aim of this contribution is to derive a general matrix formula for the
net period premium paid in more than one state. For this purpose we propose to
combine actuarial technics with the graph optimization methodology. The
obtained result is useful for example to more advanced models of dread disease
insurances allowing period premiums paid by both healthy and ill person (e.g.
not terminally yet). As an application, we provide analysis of dread disease
insurances against the risk of lung cancer based on the actual data for the
Lower Silesian Voivodship in Poland.
