Market Dynamics. On Supply and Demand Concepts

The disbalance of Supply and Demand is typically considered as the driving force of the markets. However, the measurement or estimation of Supply and Demand at price different from the execution price is not possible even after the transaction. An approach in which Supply and Demand are always matched, but the rate $I=dv/dt$ (number of units traded per unit time) of their matching varies, is proposed. The state of the system is determined not by a price $p$, but by a probability distribution defined as the square of a wavefunction $\psi(p)$. The equilibrium state $\psi^{[H]}$ is postulated to be the one giving maximal $I$ and obtained from maximizing the matching rate functional $<I\psi^2(p)>/<\psi^2(p)>$, i.e. solving the dynamic equation of the form "future price tend to the value maximizing the number of shares traded per unit time". An application of the theory in a quasi--stationary case is demonstrated. This transition from Supply and Demand concept to Liquidity Deficit concept, described by the matching rate $I$, allows to operate only with observable variables, and have a theory applicable to practical problems.