A Multiple State Model for Premium Calculation when Several Premium-Paid States are Involved

Abstract

The aim of this contribution is to derive a general matrix formula for the net
period premium paid in more than one state. In order to avoid “overpayment”
which implies higher premiums we give a formula for replacement of lump sum
benefit into annuity benefits paid in more than one state. 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 supply analysis of dread disease insurances against the
risk of lung cancer based on the actual data for the Lower Silesian Voivodship
in Poland.