Equilibrium of decision-making process in financial market

The stochastic process of a financial market is influenced by decisions of investors. The behavior of the investors somehow determines the movement pattern of the market. On the other hand, the movement observed in market can also have impact on the decision-making process of investors. This makes it possible for every kind of decisions to have a tendency to compete with other decisions on the probability of being used. The consequence of this competition is equilibrium in the distribution of probability for each decisions to take actions. To start with, a model with single factor is established to prove the existence of the equilibrium. The model shows that the convergence of the probability distribution does exist. For a more complex market with multifactor, the form of decision-making processes will be shown in a more abstract way. We invite the mathematical concept from abstract algebra to describe the framework of a multifactor market. The existence of the probability distribution is proved to be true under some given conditions.