  The paper studies pricing of insurance products focusing on the pricing of
annuities under uncertainty. This pricing problem is crucial for financial
decision making and was studied intensively, however, many open questions still
remain. In particular, there is a so-called "annuity puzzle" related to certain
inconsistency of existing financial theory with the empirical observations for
the annuities market. The paper suggests a pricing method based on the risk
minimization such that both producer and customer seek to minimize the mean
square hedging error accepted as a measure of risk. This leads to two different
versions of the pricing problem: the selection of the annuity price given the
rate of regular payments, and the selection of the rate of payments given the
annuity price. It appears that solutions of these two problems are different.
This can contribute to explanation for the "annuity puzzle".
