ABSTRACT
This chapter concerns pension models. We have already considered the simplest one in Section 10.1.2.1 (see, in particular, the last position in Table 1 there), where the level deferred annuity may be viewed as future pension payments, and the temporal premium annuity as contributions to a retirement account. In this case, the benefit premium is a net contribution rate of the participant’s payments for having a retirement annuity in the future, provided that the participant will survive the retirement age. As we saw in Table 1 mentioned, for example in the discrete time case, the net contribution rate (premium) per one unit of the future pension rate equals
a¨x:n =
;
where x is the participant’s age at the moment of entering the pension plan and n is the time to retirement. In reality, the situation is much more complicated for many reasons. In particular, the
future pension as well as the contributions to a retirement account may depend on the (changing in time) salary of the future retiree; the pension may depend on the age of the participant and may change in time due to inflation. This and other features will be reflected in models below. When an actuary is analyzing a pension plan, her/his main task is to check the plan’s sol-
vency and provide conditions ensuring a certain balance between future benefit payments and present contributions to a retirement account. Due to the law of large numbers, such a balance may be achieved more easily if individual pension plans do not run separately but rather are parts of a common fund including many participants. The corresponding models in this case are more developed and are also considered below.
