### Abstract

Original language | English |
---|---|

Number of pages | 23 |

Journal | Physica Scripta |

Volume | 90 |

Publication status | Published - 2015 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Atomic and Molecular Physics, and Optics
- Mathematical Physics
- Condensed Matter Physics

### Cite this

*Physica Scripta*,

*90*.

**Toward a formalization of a two traders market with information exchange.** / Bagarello, Fabio; Bagarello; Haven.

Research output: Contribution to journal › Article

*Physica Scripta*, vol. 90.

}

TY - JOUR

T1 - Toward a formalization of a two traders market with information exchange

AU - Bagarello, Fabio

AU - Bagarello, null

AU - Haven, null

PY - 2015

Y1 - 2015

N2 - This paper shows that Hamiltonians and operators can also be put to good use even in contexts which are not purely physics based. Consider the world of finance. The work presented here models a two traders system with information exchange with the help of four fundamental operators: cash and share operators, a portfolio operator, and an operator reflecting the loss of information. An information Hamiltonian is considered and an additional Hamiltonian is presented which reflects the dynamics of selling/buying shares between traders. An important result of the paper is that when the information Hamiltonian is zero, portfolio operators commute with the Hamiltonian and this suggests that the dynamics are really due to the information. Under the assumption that the interaction and information terms in the Hamiltonian have similar strength, a perturbation scheme is considered on the interaction parameter. Contrary to intuition, the paper shows that up to a second order in the interaction parameter, a key factor in the computation of the portfolios of traders will be the initial values of the loss of information (rather than the initial conditions on the cash and shares). Finally, the paper shows that a natural outcome from the inequality of the variation of the portfolio of trader one versus the variation of the portfolio of trader two, begs for the introduction of 'good' and 'bad' information. It is shown that 'good' information is related to the reservoirs (where an infinite set of bosonic operators are used) which model rumors/news and external facts, whilst 'bad' information is associated with a set of two modes bosonic operators.

AB - This paper shows that Hamiltonians and operators can also be put to good use even in contexts which are not purely physics based. Consider the world of finance. The work presented here models a two traders system with information exchange with the help of four fundamental operators: cash and share operators, a portfolio operator, and an operator reflecting the loss of information. An information Hamiltonian is considered and an additional Hamiltonian is presented which reflects the dynamics of selling/buying shares between traders. An important result of the paper is that when the information Hamiltonian is zero, portfolio operators commute with the Hamiltonian and this suggests that the dynamics are really due to the information. Under the assumption that the interaction and information terms in the Hamiltonian have similar strength, a perturbation scheme is considered on the interaction parameter. Contrary to intuition, the paper shows that up to a second order in the interaction parameter, a key factor in the computation of the portfolios of traders will be the initial values of the loss of information (rather than the initial conditions on the cash and shares). Finally, the paper shows that a natural outcome from the inequality of the variation of the portfolio of trader one versus the variation of the portfolio of trader two, begs for the introduction of 'good' and 'bad' information. It is shown that 'good' information is related to the reservoirs (where an infinite set of bosonic operators are used) which model rumors/news and external facts, whilst 'bad' information is associated with a set of two modes bosonic operators.

UR - http://hdl.handle.net/10447/147440

UR - http://iopscience.iop.org/1402-4896/90/1/015203/pdf/1402-4896_90_1_015203.pdf

M3 - Article

VL - 90

JO - Physica Scripta

JF - Physica Scripta

SN - 0031-8949

ER -