Development of a contextual non-classical (quantum physics based) theory for financial option pricing and for modeling a socio-economic system

AIM

The goal is to adopt the mathematical formalism of quantum mechanics to model socio-economic systems incorporating their emergent, contextual and non-deterministic aspects. As a specific application of this approach in economics, we consider non-classical models for financial option pricing. Inspired by a quantum mechanical formalism to model concepts and their disjunctions and conjunctions, we follow in this project a specific hypothesis. Namely that within human decision making two superposed layers can be distinguished:

• a layer guided by an underlying classical deterministic process, giving rise to essentially classical Boolean logical thought and its indeterministic version modeled by classical probability theory;
• a layer guided by conceptual weights of different types, such as ‘typicality’, ‘membership’, ‘representativeness’, ‘similarity’, ‘applicability’, ‘preference’ or ‘utility’, giving rise to ‘conceptual thought’, which is indeterministic in essence, but equally well, although very differently, organized than logical thought.

A substantial part of the conceptual thought process can be modeled by quantum mechanical probabilistic structures. We consider examples of this interdisciplinary approach in economics where the effects of the presence of this ‘conceptual thought’ and its deviations from classical logical thought have been noticed and studied, e.g. Allais and Ellsberg paradox.

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