  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.
