1. Actuality of theme of research
2. Purpose and research tasks
3. Subject and object of research
4. Scientific novelty
5. Practical value
6. Research prospects

The increasing role of financial factor in functioning of the production economic systems (PES) presently is one of the most personal touches of economic life of countries with the developed market economics. Experience of the Ukrainian enterprises confirms this position: their competitiveness and solvency in a great deal are determined by rational organization of finances. Financial activity of enterprises must be organized so that to be instrumental in the rise of efficiency of production due to monitoring of dynamic changes of external economic environment determining his conduct, and adequate reaction on these changes on the base of modern conceptions of management and new information technologies.
Thus, functioning of finances of enterprises must be carried out on the basis of purposeful their organization, and the dynamic management by a financial subsystem becomes important and inalienable part of the system of the PES management and is directed on the rise of efficiency of its functioning. Wherein to the questions of monitoring and rise of dynamic quality, flexibility, vitality and, in final analysis, real efficiency of functioning of the financial subsystem PES is not spared sufficient attention in the process of management the considerable non-productive distraction of financial resources is beforehand well-to-do.
Dynamic case frames by financial resources, based on the known optimization models, became the classic example of application of mathematical methods in economics. These researches found the sufficient reflection in works of both home and foreign authors, such, as well as I. A. Blank, V. M. Glushkov, V. A. Zabrodskiy, Yu. G. Lisenko, V. L. Petrenko, G. Gandolfo, B. Kollas, P. A. Samuelson, R. M. Solou, G. R. Hiks, because of what in them the specific of tasks of management by financial resources is taken into account, operations analyses in an economics, theories of inventory control, etc.
Actuality of the adopted problems, stimulated the necessity of creation of the effective and structural dynamic system of management by the financial subsystem of enterprise choice of theme of the given research, his purpose and tasks.

The research purpose is Development of the dynamic complex system of financial management of the production economic systems in the conditions of aggressive economic surroundings. For achievement of this purpose the following tasks are put and decided in work:

• the analysis of existent models of research of dynamics of functioning of the financial subsystem PES is executed;
• the systems analysis of functioning of the financial system PES is conducted, functions and structure of the system of financial management are formalized;
• conception of the dynamic system of the PES financial management is developed;
• the mathematical model of financial streams on the basis of monitoring of the state of the financial activity PES is developed;
• a case frame by the system dynamics of the PES finances is developed;
• the method of construction of the informative system of support of flexible financial decisions is developed.

The dynamic processes of management by the financial system of PES are a research object.
The subject of research is contained within the framework of object. It is models and methods used in the system of the PES financial management.

In work raising and decision of a new actual task of design of dynamics of processes of financial management of the production economic system is carried out. The following scientific results are thus got:

• conception of the dynamic system of the PES financial management, built on the basis of application of basic ideas of theory of management by a firm, offered by St. Bir, and methods of the PES management by objectives, which allows to react adequately on revolting influences of aggressive external environment;
• mathematical model of financial streams, built with the use of basic ideas of controlling and allowing to promote exactness and authenticity of information for acceptance of effective financial decisions;
• case frames by the PES finances, which use the ideas of method of system dynamics, and which provide the developed dynamic flexibility to the financial system;
• method of construction of the informative system for support of flexible financial decisions, developed with the use of modern information technologies and providing the required exactness and operative of preparation of information.

The value of the computations of research, got in work, consists in the following:

• offered in master's degree work conception of the dynamic system of the PES financial management allows to react adequately on revolting influences of aggressive external environment and complex of economic mathematical models and methods of their realization allow to go out on a high-quality new level of providing of efficiency of financial activity of the production economic systems;
• the offered complex of models and methods of their realization has high universality and can be used for the management by any production economic systems, and also, with definite limitations, by the systems of the unproductive setting.

The further deep study of models of the aggregated co-operation of enterprises in a macroeconomic aspect is recommended. Construction of statistical models of prognostication of efficiency and eventual results of activity is assumed for separate enterprises and industries.