Arraut, IvanIvanArrautAu, AlanAlanAuTse, Alan Ching-biuAlan Ching-biuTseLobo Marques, Joao AlexandreJoao AlexandreLobo Marques2024-04-022024-04-022020https://dspace.usj.edu.mo/handle/123456789/4835It 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.enGeneral Financetext::journal::journal article