Paper: arXiv 2507.05287

Authors: Davit Gondauri

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.

Complexity vs Empirical Score

  • Math Complexity: 7.5/10
  • Empirical Rigor: 5.0/10
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper presents an ambitious attempt to adapt the nonlinear fluid dynamics of Navier-Stokes equations to macroeconomic liquidity flows and systemic risks using Georgian statistical data (2010–2024). While mathematically novel and mathematically intensive, its empirical validation relies heavily on dynamic residual balancing and heuristic AI-tuning, which slightly diminishes its empirical rigor and reproducibility.

Research Flowchart

  flowchart TD
    A["<b>Research Goal</b><br>Model liquidity flows & systemic risk using modified Navier-Stokes equations"] --> B["<b>Data Inputs (Georgia 2010-2024)</b><br>13 Macro/Financial params: GDP, Inflation, Gini, CDS, LCR"]
    B --> C["<b>Core Methodology</b><br>Modified Navier-Stokes modeling with 13 macroeconomic parameters"]
    C --> D["<b>Computational Framework</b><br>Fourier analysis, stochastic simulation & AI-based calibration"]
    D --> E["<b>Key Outcomes</b><br>Accurate liquidity/risk forecasting & countercyclical policy planning"]