GAME MODEL FOR SECURITIES TRADING PROCESS CONTROL

Abstract

A game model of a trading session (TS) on the securities market is proposed. It is advisable to describe the controllability of the TS process from the point of view of the game approach. It is proposed to use a bilinear differential quality game to solve this problem. The use of bilinear differential games is due to the use of the financial resources allocating procedure, which is an integral component of the securities purchase and sale process control. However, neither the first direct method nor the alternating integral method of L.S. Pontryagin is applicable, since the Cauchy formula is not applicable here. In addition, the methods of N.N. Krasovsky’s school, in particular, the construction of stable bridges, are not applicable, despite the existing meaning of “small game”. Therefore, the article used a discrete approximation method, which allows overcoming the above difficulties and finding an analytical solution in explicit form. Novelty of the problem - description of the dynamics of the securities purchase and sale process control and its consideration in continuous time, which allows having a procedure qualitative assessment. Zones of bullish and bearish trends important for decision-making by investors were found. The results of the work may be useful for preventing situations of price instability in the securities investments market contributing to the efficient operation of departments supervising the securities purchase and sale process and to the development of control actions to maintain price stability at the level of large banking players, and can also be used in computer DSS when investors are searching for a constructive strategy. The results of a computational experiment performed in the MatLab simulation environment are presented.