The formulation of quantum mechanics as a diffusion process by Nelson provides for an interesting approach on how we may transit from classical mechanics into quantum mechanics. Besides the presence of the real potential function, another type of potential function forms an intrinsic part of this theory. In this paper we attempt to show how both types of potential functions can have a use in a resolutely macroscopic context like financial asset pricing. We are particularly interested in uncovering how the (...) ‘quantum potential’ can add to the economics-based relevant information which is already supplied by the real potential function. (shrink)

q-derivatives are part of so called quantum calculus. In this paper we investigate how such derivatives can possibly be used in Itô’s lemma. This leads us to consider how such derivatives can be used in a social science setting. We conclude that in a Itô Lemma setting we cannot use a macroscopic version of the Heisenberg uncertainty principle with q-derivatives.

Under certain conditions private information can be a source of trade. Arbitrage for instance can occur as a result of the existence of private information. In this paper we want to explicitly model information. To do so we define an ‘information function’. This information function is a mathematical object, also known as a so called ‘wave function’. We use the definition of wave function as it is used in quantum mechanics and we attempt to show the usefulness of this wave (...) function in an economic context. We attempt to answer the following questions. How does the information function relate to private information? How can we use the information function to define the ‘quantity’ of information? How can we use the information function in arbitrage-based option pricing? How can the information function be used in the formulation of a so called Universal Brownian motion? (shrink)