A quantum mechanical model for the rate of return

TL;DR

This paper introduces a quantum mechanical model for the rate of return in financial markets, treating it as a quantized variable with a finite-dimensional Hilbert space, and describes its evolution via a Schrödinger-like equation.

Contribution

It proposes a novel quantum framework for modeling the rate of return, incorporating quantization and non-observability aspects not addressed by classical models.

Findings

The rate of return is modeled as a discrete wave function.

The evolution of the rate of return follows a Schrödinger-type equation.

The model captures the quantized nature of financial returns.

Abstract

In their activity, the traders approximate the rate of return by integer multiples of a minimal one. Therefore, it can be regarded as a quantized variable. On the other hand, there is the impossibility of observing the rate of return and its instantaneous forward time derivative, even if we consider it as a continuous variable. We present a quantum model for the rate of return based on the mathematical formalism used in the case of quantum systems with finite-dimensional Hilbert space. The rate of return is described by a discrete wave function and its time evolution by a Schodinger type equation.