ABSTRACT
In Chapters 2 and 3, we already considered premium determination; more precisely, premiums ensuring the solvency of insurance mechanisms. The models of those chapters concerned short-term insurance and single premiums; that is, premiums paid just one time at the beginning of the period under consideration. As has been already mentioned in Section 2.4, in the case of life insurance or future annu-
ities, for example, pension plans, the policies are based not on single premiums but rather on sequences of premium payments to be carried out at certain rates. We will call such sequences of payments premium annuities. In this case, when determining a premium rate, the company usually proceeds from the total future random loss, which is the difference between the payments the company will provide in accordance with the contract and the total amount of premiums the company will receive until the contract is terminated. The corresponding models are explored in Section 1. After we have considered problems concerning premiums, we will proceed-in Section
2-to the notion of reserve, which may be defined as the value of the future liability of the insurer.
