ABSTRACT
An annuity is a series of payments made at certain intervals (as months or years) during some period which is, as a rule, random. Typical examples are pensions which are life annuities paid while the retired person lives, or an alimony which is paid until one of spouses dies. As a good (and often convenient) approximation, actuaries use also models where annu-
ity payments are carried out in a continuous-time fashion. Regular payment of premiums by an insured, say, in the case of life insurance, is also an
annuity. In this case, the annuitant-that is, the party receiving the annuity-is the insurance company, while the single payment of benefits constitutes the losses of the company. Accumulated values, though they are strongly connected with annuities, will be consid-
ered in Section 10.1.3 after we consider the notion of a net premium rate. Below, we systematically explore two models: continuous-time and those where pay-
ments are provided at the beginning of certain periods, that is, in a discrete way.
