Emergence of fuzzy preferences for risk in a Birkhoff-von Neumann logics environment

We show that if a portfolio of a financial derivative asset and a stock is put in an environment where the value of an asset (besides its price) is formalized as a superposition of price states, such portfolio may not be risk free and fuzzy preferences for risk premia may exist. We argue for a modification of the classical Brownian motion process as used in option pricing. This modification on the classical Brownian motion, we call the ℏ^-Brownian motion and one specific format of this ℏ^-Brownian motion can be shown to have a connection with the quantum physical Schrödinger equation.