Model-based and empirical analyses of stochastic fluctuations in economy and finance

ArXiv ID: 2408.16010 “View on arXiv”

Authors: Unknown

Abstract

The objective of this work is the investigation of complexity, asymmetry, stochasticity and non-linearity of the financial and economic systems by using the tools of statistical mechanics and information theory. More precisely, this thesis concerns statistical-based modeling and empirical analyses with applications in finance, forecasting, production processes and game theory. In these areas the time dependence of probability distributions is of prime interest and can be measured or exactly calculated for model systems. The correlation coefficients and moments are among the useful quantities to describe the dynamics and the correlations between random variables. However, the full investigation can only be achieved if the probability distribution function of the variable is known; its derivation is one of the main focuses of the present work.

Keywords: Statistical Mechanics, Information Theory, Probability Distributions, Correlation Coefficients, Stochasticity, General Financial/Economic Systems

Complexity vs Empirical Score

• Math Complexity: 7.5/10
• Empirical Rigor: 4.0/10
• Quadrant: Lab Rats
• Why: The thesis employs advanced statistical mechanics and information theory with heavy mathematical derivations (saddle point methods, exact probability distributions, entropy/MI calculations) but focuses on theoretical model-based analyses and standard empirical studies (correlations, VIX analysis) without demonstrating backtest-ready implementation or complex data pipelines.

  flowchart TD
    A["Research Goal<br>Investigate complexity, asymmetry, and<br>stochasticity in financial/economic systems"] --> B["Methodology<br>Statistical Mechanics & Information Theory"]
    
    B --> C["Data/Inputs<br>Financial/Economic Time Series<br>(Production, Market, Game Data)"]
    
    C --> D["Computational Process<br>Modeling & Empirical Analysis"]
    
    subgraph D ["Key Tools & Processes"]
        D1["Probability Distribution Functions"]
        D2["Correlation Coefficients & Moments"]
        D3["Time-Dependent Analysis"]
    end
    
    D --> E["Key Findings/Outcomes<br>Stochastic Fluctuations Characterized<br>System Dynamics Quantified<br>Forecasting Models Validated"]
    
    D1 --> D
    D2 --> D
    D3 --> D