Using Fermat-Torricelli points in assessing investment risks

TL;DR

This paper explores how Fermat-Torricelli points can be used to analyze complex investment risk data, reducing noise and accounting for non-normal distributions in financial series.

Contribution

It introduces a novel application of Fermat-Torricelli points for smoothing and analyzing financial time series with high variance and nonlinear trends.

Findings

Fermat-Torricelli points effectively reduce the influence of randomness in financial data.

The method accounts for non-normal distribution characteristics of long-term financial series.

External factors significantly impact the distribution properties of investment risk data.

Abstract

The use of Fermat-Torricelli points can be an effective mathematical tool for analyzing numerical series that have a large variance, a pronounced nonlinear trend, or do not have a normal distribution of a random variable. Linear dependencies are very rare in nature. Smoothing numerical series by constructing Fermat-Torricelli points reduces the influence of the random component on the final result. The presence of a normal distribution of a random variable for numerical series that relate to long time intervals is an exception to the rule rather than an axiom. The external environment (international economic relations, scientific and technological progress, political events) is constantly changing, which in turn, in general, does not give grounds to assert that under these conditions a random variable satisfies the requirements of the Gauss-Markov theorem.