Optimum Equalization Principle Applied to the Financial Arbitrage Model. The Entropic Settlement of Coalitions within Partial Cooperative Games

摘要

The financial arbitration model was introduced by Ross [8] in the analysis of the capital profitability owned by an active portfolio. At first, the profitability of an active portfolio was analyzed taking into consideration a single factor, which is the risk factor. The risk was estimated with the help of a statistical indicator which is represented by the mean square deviation. Practically, a separation theorem was formulated through which the investment zone (active buyers), the zone of maintaining the investment and the active sales zone can be delimited. Based on this result, the so-called "safety line of the market" could be defined; it is an extremely important element in different financial calculation. But the financial arbitration model implies taking into consideration other factors of influence (beside the risk factor) in analyzing the profitability of an active portfolio. Moreover, it is also considered the possibility to modify the portfolio structure without any investment intervention on actives and the average profitability of the portfolio should increase only by changing the active's weight. Another important element regarding this paper is represented by the practicability of the results concerning the way coalitions are formed within a partial cooperative decisional process. This problem, extremely important within the context of game theory, is solved by means of equalization principle. Thus, we shall consider the degree of organization for a system as the efficiency function, and we shall define this function by using an entropic approach.