Quantum Continuous Gradient Models in the Study of Markets

Abstract

Business students graduate without knowing about the existence of quantum continuous gradient models (QCGM) to study financial markets. This paper introduces and discusses these models. The underlying function space Map (X, Y) of QCGM is a set of smooth maps called envelope-gradient functions (EGF) from X to Y with the standard compact-open topology. Herein, we take advantage of some natural properties of EGF to define a classical associative algebra on it and develop a mathematical QCGM. The development of QCGM involves principles of deformation quantization theory and definite integrals of EGF on uniform probability distributions. Applications in economics and further lines of research are suggested.