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Recently financial mathematics has a period of deep progress. It uses welldeveloped mathematic methods to describe different economic situations, moreover it uses both probability theory and control theory.

The decision-making problems are very important for financial management, so we can use the theory of the optimal control for modeling different situations. The basic methods of finding the optimal control (in this models) are: Pontryagin’s maximum principle and method of the dynamic programming. Many of this models are simple to analyse and you can get good results from such analisis.

The researchers didn’t take into consideration the phenomenon of time delay in first decision-making models [1,2]. But this phenomenon is very important to make the model true to life, in spite of the fact that it makes the analisis more difficult.

Progress of the theory of the equations with delay made such analisis simpler, because there had been found general solutions for different equations with delay, stability of these solutions, etc.

The phenomenon of time delay was considered in [3] (the equations in the model had the form of the equations with time delay - it showed that the interest could not be obtained immediately, it could only be obtained after some time), but the author neglected the fact that the bond price depends on conditions of the securities market. This model describes such problem of the decision-makers of some units (families, firms): part of their money must be reserved in a bank as a current deposit so that it can be used at any time they need it, while the other part can be used to buy bonds (to get more interest). They must buy bonds in moderate amounts, for if they buy too many, when they need money, they have sell some bonds and then must pay more money to the bonddealers. From this reason we can see that the mount of the bonds they buy is very important.

We changed this model (considered all the abovementioned remarks), gave general solution and some steps how could this model be improved.