A Non-Stochastic Special Model of Risk Based on Radon Transform

Abstract

The concept of risk is fundamental in various scientific fields, including physics, biology and engineering, and is crucial for the study of complex systems, especially financial markets. In our research, we introduce a novel risk model that has a natural transactional–financial interpretation. In our approach, the risk of holding a financial instrument is related to the measure of the possibility of its loss. In this context, a financial instrument is riskier the more opportunities there are to dispose of it, i.e., to sell it. We present a model of risk understood in this way, introducing, in particular, the concept of financial time and a financial frame of reference, which allows for associating risk with the subjective perception of the observer. The presented approach does not rely on statistical assumptions and is based on the transactional interpretation of models. To measure risk, we propose using the Radon transform. The financial concept of risk is closely related to the concepts of uncertainty, entropy, information, and error in physics. Therefore, the well-established algorithmic aspects of the computed tomography method can be effectively applied to the broader field of uncertainty analysis, which is one of the foundational elements of experimental physics.