Regardless of the type of insurance the basic part of the insurance premium is the pure premium, often referred to as net premium, which is based on the risk of death of the insured, averaged over the entire insurance period. The net premium is therefore the fund amount that the insured should pay in order for the insurer to possess sufficient funds to cover all benefits during the contract period. In accordance with the principles of actuarial mathematics the valuation of standard life insurance is based on the equivalence principle and takes into account the risk of death and also the change in time value of money, i.e. actuarial risk, which is estimated by the insurer at the time of signing the contract. Such method of calculating the net premium does not ensure the protection of collected funds against aggregated and individual longevity risk, which may negatively affect long-term financial stability of insurers as well as the level of financial security of the insured. Hence it is necessary to, on the one hand precisely valuate the trend of further life expectancy, and on the other there is a need to modify the methods of calculating premium rates and their adjustment in the duration of the contract. Therefore the article includes premium calculations that take into account the extended actuarial risk that encompasses longevity risk and its effect on their amount. This problem is the aim of the analysis carried out in the article. That is to say, taking into account the extended actuarial risk that encompasses longevity risk, a fair premium formula including the need for a risk adjustment was presented, followed by a premium calculation based on the example of life insurance with the AI and ADI option, as well as a look into the effect of change in longevity risk on their amount.

multi-state life insurance, longevity risk, premium