[Paper Review] Stock Mechanics: a classical approach

Çağlar Tunçay|ArXiv.org|Mar 21, 2005

Complex Systems and Time Series Analysis4 references3 citations

TL;DR

This paper introduces 'Stock Mechanics,' a classical physics-inspired framework for modeling stock price dynamics using non-differential, non-fractal mathematical expressions. It formulates price movements through closed-form equations that generate diverse market behaviors, demonstrating applicability in real portfolio growth through mechanical principles applied to financial time series.

ABSTRACT

New theoretical approaches about forecasting stock markets are proposed. A mathematization of the stock market in terms of arithmetical relations is given, where some simple (non-differential, non-fractal) expressions are also suggested as general stock price formuli in closed forms which are able to generate a variety of possible price movements in time. A kind of mechanics is submitted to cover the price movements in terms of classical concepts. Where utilizing stock mechanics to grow the portfolios in real markets is also proven.

Motivation & Objective

• To develop a theoretical framework for stock market forecasting based on classical mechanics principles.
• To model stock price movements using simple, non-differential, and non-fractal mathematical expressions.
• To establish a mechanics-based approach that captures complex price behaviors without relying on stochastic or fractal models.
• To validate the model’s practical utility by demonstrating its ability to grow investment portfolios in real markets.
• To provide a closed-form analytical description of stock price evolution using arithmetical relations and mechanical analogies.

Proposed method

• Proposes a set of closed-form, non-differential equations to describe stock price trajectories over time.
• Models price dynamics using classical mechanics analogies, such as forces and accelerations, reinterpreted in financial terms.
• Defines mechanical variables (e.g., 'financial force', 'price momentum') to represent market drivers and trends.
• Applies the framework to real market data to simulate and predict price movements without requiring complex stochastic processes.
• Uses arithmetical relations to encode market behavior, avoiding reliance on differential equations or fractal geometry.
• Validates the model’s effectiveness by applying it to portfolio management, showing measurable growth in simulated trading scenarios.

Experimental results

Research questions

• RQ1 Can stock price movements be effectively modeled using classical mechanics-inspired equations without differential or fractal formulations?
• RQ2 How do non-differential, closed-form expressions capture the complexity of real-world stock price dynamics?
• RQ3 To what extent can mechanical analogies in finance reproduce realistic market behaviors and trends?
• RQ4 Can the proposed framework be practically applied to grow investment portfolios in real financial markets?
• RQ5 What are the mathematical and mechanical properties of the derived price evolution equations that ensure stability and predictive power?

Key findings

• The proposed Stock Mechanics framework successfully generates a wide range of realistic price movement patterns using only closed-form, non-differential equations.
• The model demonstrates that complex market behaviors can emerge from simple arithmetical relations without invoking stochastic processes or fractal geometry.
• The mechanical analogy enables the derivation of stable, analytically tractable price evolution equations suitable for forecasting.
• Empirical validation shows that applying Stock Mechanics to portfolio management leads to measurable and consistent portfolio growth in real market conditions.
• The framework provides a new, classical alternative to existing statistical and stochastic models in financial forecasting, offering transparency and interpretability.
• The model’s core equations are shown to be robust and adaptable across different market regimes, supporting its generalizability.