If a Riemann sum limit type quantum integral I is defined on a subspace of a filtrated *-algebra B acting on a separable Hilbert space H , we show that one can construct a quantum finance model, representing a financial market of finitely many basic assets whose numeraire normalized values are {(Xi (t))t0}di=1 as a filtrated von Neumann algebra A of bounded operators on H . A fundamental asset pricing theorem states that the market is arbitrage free if and only if there exists a faithful normal state rho in the predual A of A such that each (Xi (t)t0 is a rho-martingale. This allows one to assign fair prices to European contingent claims written on these basic assets in the market.A quantum finance model of this kind is established where I is the quantum stochastic integrals defined by the canonical unbounded quantum noises acting on a Boson Fock space. Two additional quantum finance models are sketched in this note. In the first model, the integration I is defined through the standard bounded quantum noises acting on a free Fock space. The quantum Brownian motions on two Fock spaces are tensor independent and free independent, free in the sense, respectively. The second model in this note is an abstraction of the above two when the quantum noises are Brownian motions. Utilizing the quantum integral theory on non-commutative Lp-space, we focus on a multi-factor free Brownian motion quantum finance model.