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

Authors:
Emmanuel Haven
Affiliations:
Department of AFM, University of Essex, Wivenhoe Park, Colchester C04 3SQ,UK
Venue:
Fuzzy Sets and Systems
Year:
2005

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Abstract

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 @?@^-Brownian motion and one specific format of this @?@^-Brownian motion can be shown to have a connection with the quantum physical Schrodinger equation.