TY - JOUR
TI - The Probability Flow in the Stock Market and Spontaneous Symmetry Breaking in Quantum Finance
AU - Arraut, Ivan
AU - Lobo Marques, João Alexandre
AU - Gomes, Sergio
T2 - Mathematics
AB - The spontaneous symmetry breaking phenomena applied to Quantum Finance considers that the martingale state in the stock market corresponds to a ground (vacuum) state if we express the financial equations in the Hamiltonian form. The original analysis for this phenomena completely ignores the kinetic terms in the neighborhood of the minimal of the potential terms. This is correct in most of the cases. However, when we deal with the martingale condition, it comes out that the kinetic terms can also behave as potential terms and then reproduce a shift on the effective location of the vacuum (martingale). In this paper, we analyze the effective symmetry breaking patterns and the connected vacuum degeneracy for these special circumstances. Within the same scenario, we analyze the connection between the flow of information and the multiplicity of martingale states, providing in this way powerful tools for analyzing the dynamic of the stock markets.
DA - 2021/01//
PY - 2021
DO - 10.3390/math9212777
DP - www.mdpi.com
VL - 9
IS - 21
SP - 2777
LA - en
SN - 2227-7390
UR - https://www.mdpi.com/2227-7390/9/21/2777
Y2 - 2022/09/21/05:00:55
KW - Hermiticity
KW - conservation of the information
KW - degenerate vacuum
KW - flow of information
KW - martingale condition
KW - random fluctuations
KW - spontaneous symmetry breaking
KW - vacuum condition
ER -
TY - JOUR
TI - On the probability flow in the Stock market I: The Black-Scholes case
AU - Arraut, Ivan
AU - Au, Alan
AU - Tse, Alan Ching-biu
AU - Marques, Joao Alexandre Lobo
T2 - arXiv.org
AB - 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.
DA - 2020///
PY - 2020
DP - ProQuest
VL - 1
SP - 1
EP - 10
LA - English
ST - On the probability flow in the Stock market I
UR - https://search.proquest.com/docview/2332255379?pq-origsite=primo
Y2 - 2021/02/03/07:58:09
KW - General Finance
ER -