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.

Accurate determination of the probability structure of the multistate model is significant from the valuation and profitability assessment of insurance contracts standpoint. This article aims to analyse the effect of spouses' future lifetime dependence on premiums and prospective reserves for marriage insurance contracts. As a result, under the assumptions that the evolution of the insured risk is described by a nonhomogeneous Markov chain and the dependence between spouses' future lifetime is modelled by the copula, we derive formulas for the elements of the transition matrices. Based on actual data, we conduct a comparative analysis of actuarial values for three scenarios related to future lifetimes of husband and wife. We test the robustness of premium value to the changing degree of dependency between spouses' future lifetimes.