The probability flow in the Stock market and Spontaneous symmetry breaking in Quantum Finance
arXiv:2206.07130 · doi:10.3390/math9212777
Abstract
The Spontaneous Symmetry breaking in Quantum Finance considers the martingale condition in the stock market as a vacuum state if we express the financial equations in the Hamiltonian form. The original analysis for this phenomena ignores completely 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 market.
arXiv comment15 pages, preprint of a published version. arXiv admin note: substantial text overlap with arXiv:2004.11270
References in corpus (12)
- A Path Integral Approach to Option Pricing with Stochastic Volatility: Some Exact Results
- Symmetries and conservation laws in non-Hermitian field theories
- Spontaneous symmetry breaking and the Goldstone theorem in non-Hermitian field theories
- Gauge invariance and the Englert-Brout-Higgs mechanism in non-Hermitian field theories
- Hamiltonian and Potentials in Derivative Pricing Models: Exact Results and Lattice Simulations
- Reduced density matrix and order parameters of a topological insulator
- The Quantum Yang Baxter conditions: The fundamental relations behind the Nambu-Goldstone theorem
- The Nambu-Goldstone theorem in non-relativistic systems
- Spontaneous symmetry breaking in Quantum Finance
- Density Matrix Spectra and Order Parameters in the 1D Extended Hubbard Model
- The connection between multiple prices of an Option at a given time with single prices defined at different times: The concept of weak-value in quantum finance
- Construct order parameter from the spectra of mutual information