Why Bohmian Approach to Quantum Econometrics: An Algebraic Explanation

Abstract

© Springer Nature Switzerland AG 2020. Many equations in economics and finance are very complex. As a result, existing methods of solving these equations are very complicated and time-consuming. In many practical situations, more efficient algorithms for solving new complex equations appear when it turns out that these equations can be reduced to equations from other application areas—equations for which more efficient algorithms are already known. It turns out that some equations in economics and finance can be reduced to equations from physics—namely, from quantum physics. The resulting approach for solving economic equations is known as quantum econometrics. In quantum physics, the main objects are described by complex numbers; so, to have a reduction, we need to come up with an economic interpretation of these complex numbers. It turns out that in many cases, the most efficient interpretation comes when we separately interpret the absolute value (modulus) and the phase of each corresponding quantum number; the resulting techniques are known as Bohmian econometrics. In this paper, we use an algebraic approach—namely, the idea of invariance and symmetries—to explain why such an interpretation is empirically the best.