  It is known that the probability is not a conserved quantity in the stock
market, given the fact that it corresponds to an open system. In this paper we
analyze the flow of probability in this system by expressing the ideal
Black-Scholes equation in the Hamiltonian form. We then analyze how the
non-conservation of probability affects the stability of the prices of the
Stocks. Finally, we find the conditions under which the probability might be
conserved in the market, challenging in this way the non-Hermitian nature of
the Black-Scholes Hamiltonian.
