Dependence Modeling

Copula-based deviation measure of cointegrated financial assets ArXiv ID: 2312.02081 “View on arXiv” Authors: Unknown Abstract This study outlines a comprehensive methodology utilizing copulas to discern inconsistencies in the behavior exhibited by pairs of financial assets. It introduces a robust approach to establishing the interrelationship between the returns of these assets, exploring potential measures of dependence among the stochastic variables represented by these returns. Special emphasis is placed on scrutinizing the traditional measure of dependence, namely the correlation coefficient, delineating its limitations. Furthermore, the study articulates an alternative methodology that offers enhanced stability and informativeness in appraising the relationship between financial instrument returns. ...

Proofs that the Gerber Statistic is Positive Semidefinite ArXiv ID: 2305.05663 “View on arXiv” Authors: Unknown Abstract In this brief note, we prove that both forms of the Gerber statistic introduced in Gerber et al. (2022) are positive semi-definite. Keywords: Gerber Statistic, Positive Semi-Definite, Risk Management, Dependence Modeling, General (Risk Measurement) Complexity vs Empirical Score Math Complexity: 8.5/10 Empirical Rigor: 2.0/10 Quadrant: Lab Rats Why: The paper is dense with advanced linear algebra proofs, demonstrating matrix transformations and series expansions to establish positive semidefiniteness, which is a purely theoretical property with no practical implementation details provided. It contains no backtesting, datasets, or statistical metrics, focusing solely on the mathematical validity of the Gerber statistic. flowchart TD A["Research Goal Prove Gerber Statistic is PSD"] --> B["Analyze Structure 1-form and 2-form"] B --> C["Mathematical Derivation Matrix Factorization & Boundaries"] C --> D["Computational Verification Symbolic/Numerical Analysis"] D --> E["Key Findings Both forms are Positive Semi-Definite"] E --> F["Outcomes Validated for Risk Management & Dependence Modeling"]