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Updated: Feb 28, 2026
05:37
An R-Based Landscape Validation of a Competing Risk Model
Published on: September 16, 2022
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Crofton Risk and Relative Transactional Entropy
Marcin Makowski1, Edward W Piotrowski2
1Faculty of Physics, Department of Mathematical Methods in Physics, University of Białystok, ul. Ciołkowskiego 1L, 15-245 Białystok, Poland.
Entropy (Basel, Switzerland)
|February 27, 2026
Summary
This study introduces a geometric approach to financial risk, defining risk as exchange dilemmas from instrument trajectory intersections. This method yields a novel risk measure based on trajectory length, offering new market complexity insights.
Area of Science:
- Quantitative Finance
- Geometric Measure Theory
- Financial Mathematics
Background:
- Traditional financial risk models often lack geometric intuition.
- The annual percentage rate (APR) provides a simple model for financial instruments.
- Understanding market complexity requires novel analytical tools.
Purpose of the Study:
- To develop a novel geometric framework for quantifying financial risk.
- To introduce new concepts for analyzing market dynamics and complexity.
- To explore analogies between financial risk and thermodynamics.
Main Methods:
- Utilizing Crofton's geometric approach and the Radon transform.
- Defining financial instrument trajectories within a reference frame (money, benchmark).
- Interpreting risk as the density of intersection dilemmas with simple instruments (APR-based).
Main Results:
- A new risk measure derived from trajectory length in the Crofton-Steinhaus sense.
- Introduction of geometric volatility, transactional entropy, and trajectory temperature.
- Demonstration of thermodynamic analogies for describing market behavior.
Conclusions:
- Geometric methods offer a new perspective on financial risk assessment.
- The proposed framework enhances the understanding of market complexity.
- Thermodynamic analogies can be fruitfully applied to financial market analysis.
Keywords:
Radon transformannual percentage rate (APR)complex systementropyfinancial instrumentmarketrisktrajectory temperatureMore Related Videos
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