REFORMY (130) Financial Markets Evolution/1

9. červen 2015 | 07.00 |

Poznámka česky na konci článku.

ANALYSIS OF FINANCIAL MARKETS EVOLUTION BY UTILIZING THE THEORY OF COOPERATIVE GAMES I.

Jan Červenka, Ondřej Černík, Jiří Mihola, Radim Valenčík

Abstract

The evolution of financial markets in a long-term perspective related to changes in the society is described and analysed by utilizing the theory of cooperative games, specifically the theory of games with transferable utility and various approaches to Nash bargaining solution (S, d). The paper presents an elementary mathematical model of the financial market, an analysis of assumptions it is based on, and its transformation in the form of a cooperative game. The utilization of these mathematical means is followed by the interpretation of real actions and phenomena in the area of financial markets development. The conclusion of the paper suggests other possibilities of applying the theory of cooperative games in the respective area.

Keywords

TU-game, Nash bargaining (S, d) problem, financial markets

            JEL Classification

C7, D6

Introduction

We present tools to describe and to analyse the evolution of financial markets in a long-term perspective of dozens of years related to changes in society. We shall demonstrate that the theory of cooperative games can be effectively used to show the development of financial markets in overall social context. The core of our approach to the analysis of development tendencies of financial markets is a model based on the assumption of productive nature of consumption and non-existence of position investment:

- We formulate this model through the apparatus of mathematical analysis.

- We specify the conditions that the model is based on and point out their significance in the context of current problems and the current situation of the society.

- The basic model will be transformed in a cooperative game and its solution will be analysed by utilizing the game theory tools.

- Achieved results will be interpreted in terms of the current context of the development of financial markets.

- We suggest prospective possibilities of utilizing the theory of cooperative games in the respective area, in particular in terms of wealth split in the society (as one of the standard problems of the cooperative games theory).

The approach we have decided to take stresses the interlinking of various levels of abstraction (formulating related issues as a form of axiomatic system, utilizing the mathematical model with defined assumptions, interpretation of mathematical results, creating concepts for utilizing mathematical tools). Practical meaning of this approach lies in a better understanding of the situation resulting from the long-term evolution of financial markets, and identifying of some essential phenomena which are connected with the development of financial markets. It also refers to one of the possible approaches to the issues of social wealth split, see e.g. complex concept of this topic in the work of H. Moulin (2003).

References

[1]   Beal Sylvain, Ghintran Amandine, Remil Eric, Solal Aphilippe. The River Sharing Problem: A Survey. International Game Theory Review. 2013., Vol. 15, No. 3 (2013) 1340016 (19 pp) World Scientific Publishing Company.

[2]   Brink, René, Estévez-Fernández, Arantza, Laan, Gerard, Moes, Nigel. Independence Axioms for Water Allocation. Tinbergen Institute Discussion Paper. 2011., TI 2011-128/1

[3]   Friedman, Milton. A Theory of the Consumption Function. Princeton University Press. 1957. ISBN: 0-691-04182-2

[4]   Mlčoch, Luboš. 2007. Ekonomie a štěstí: Proč více někdy není lépe. Politická ekonomie. 2007., Vol. 54, No. 2. pp. 147-163.

[5]   Houba Harold, Laan Gerard, Zeng Yuyu. Asymmetric. Nash Solutions in the River Sharing Problem. Tinbergen Institute Discussion Paper. 2013., TI 2013-051/II

[6]   Moulin, Herv´e. Fair division and collective welfare. Massachusetts Institute of Technology. 2003. ISBN 0-262-13423-3

[7]   Štika, Petr. 2009. Ekonomie štěstí. Politická ekonomie. 2009., Vol. 56, No. 2. pp 250-262.

Poznámka v češtině:

Příspěvek byl přednesen na 7. mezinárodní konferenci VŠFS na téma "FINANČNÍ TRHY V PROCESU GLOBALIZACE SVĚTOVÉ EKONOMIKY". V češtině i s poznámkami byl zveřejněn 19.-27.4.2015 na blogu:

http://radimvalencik.pise.cz

První pokračování viz:

http://radimvalencik.pise.cz/2244-reformy-78-evoluce-financnich-trhu-1.html

(Pokračování příspěvku v angličtině)

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