Bohmian Mechanics for Financial Processes

Abstract

In this Chapter we use methods of classical and quantum mechanics for mathematical modeling of price dynamics in the financial market. The Hamil-tonian formalism on the price/price-change phase space is used to describe the classical-like evolution of prices. This classical dynamics of prices is determined by ‘hard’ conditions (natural resources, industrial production, services, and so on). These conditions as well as ‘hard’ relations between traders in the financial market are mathematically described by the classical financial potential. In the real financial market ‘hard’ conditions are not the only source of price changes. The information exchange and market psychology play important (and sometimes determining) roles in price dynamics. We propose to describe this ‘soft’ financial factors by using the pilot wave (Bohmian) model of quantum mechanics. The theory of financial mental (or psychological) waves is used to take into account market psychology. The real trajectories of prices are determined (by the financial analogue of Newton’s second law) by two financial potentials: classical-like (‘hard’ market conditions) and quantum-like (‘soft’ market conditions)¹.