The Choice of Portfolio Based on the Theory of Cooperative Games and the Zeuthen’s and Harsany’s Method

Abstract

The theory of games as a domain of mathematics is one of the methods proper for making decisions in the world of economics when we do not know how the other subjects are going to act. It seems to be a suitable tool for gambling on the stock exchange. During gambling on the stock exchange, the problem of the choice of proper portfolio appears; the player wants both great profit and low risk. It is reasonable to limit the choice only to portfolios which belong to the effective set. Then the decision of choice of a particular portfolio is individual and depends on the player and his aversion to the risk. In this article this problem is presented as the game that is, the inner conflict of the player. On the one hand he is expecting a great profit, yet on the other hand he is expecting a low risk. Which portfolio should be pointed out to give the satisfaction to the player? The solution of this problem presented in this work is based on the theory of games, which treats the search for a proper portfolio as a two-person game. A suitable game was formulated and described. The analysis of the game as a cooperative one was performed. There is also an example provided explaining the way of acting with data coming from the stock exchange in Warsaw.