Increasing Systemic Resilience to Socioeconomic Challenges: Modeling the Dynamics of Liquidity Flows and Systemic Risks Using Navier-Stokes Equations

TL;DR

This paper introduces a novel mathematical model based on Navier-Stokes equations to analyze liquidity flows and systemic risks in economic systems, validated with Georgian data from 2010-2024.

Contribution

It develops an innovative, physics-inspired model incorporating macroeconomic parameters for dynamic systemic risk assessment and forecasting.

Findings

Model effectively describes liquidity dynamics and systemic risk.

Accurately predicts extreme financial scenarios.

Provides a framework for crisis prediction and policy planning.

Abstract

Modern economic systems face unprecedented socioeconomic challenges, making systemic resilience and effective liquidity flow management essential. Traditional models such as CAPM, VaR, and GARCH often fail to reflect real market fluctuations and extreme events. This study develops and validates an innovative mathematical model based on the Navier-Stokes equations, aimed at the quantitative assessment, forecasting, and simulation of liquidity flows and systemic risks. The model incorporates 13 macroeconomic and financial parameters, including liquidity velocity, market pressure, internal stress, stochastic fluctuations, and risk premiums, all based on real data and formally included in the modified equation. The methodology employs econometric testing, Fourier analysis, stochastic simulation, and AI-based calibration to enable dynamic testing and forecasting. Simulation-based sensitivity analysis evaluates the impact of parameter changes on financial balance. The model is empirically tested using Georgian macroeconomic and financial data from 2010-2024, including GDP, inflation, the Gini index, CDS spreads, and LCR metrics. Results show that the model effectively describes liquidity dynamics, systemic risk, and extreme scenarios, while also offering a robust framework for multifactorial analysis, crisis prediction, and countercyclical policy planning.