Random Variables

Moments by Integrating the Moment-Generating Function ArXiv ID: 2410.23587 “View on arXiv” Authors: Unknown Abstract We introduce a novel method for obtaining a wide variety of moments of any random variable with a well-defined moment-generating function (MGF). We derive new expressions for fractional moments and fractional absolute moments, both central and non-central moments. The expressions are relatively simple integrals that involve the MGF, but do not require its derivatives. We label the new method CMGF because it uses a complex extension of the MGF and can be used to obtain complex moments. We illustrate the new method with three applications where the MGF is available in closed-form, while the corresponding densities and the derivatives of the MGF are either unavailable or very difficult to obtain. ...

Copulas forFinance- A Reading Guide and Some Applications ArXiv ID: ssrn-1032533 “View on arXiv” Authors: Unknown Abstract Copulas are a general tool to construct multivariate distributions and to investigate dependence structure between random variables. However, the concept of cop Keywords: Copulas, Multivariate Distributions, Dependence Structure, Random Variables, Statistical Modeling, Quantitative Methods Complexity vs Empirical Score Math Complexity: 7.5/10 Empirical Rigor: 2.0/10 Quadrant: Lab Rats Why: The paper focuses on theoretical copula constructions and dependence structures with advanced mathematics, but lacks implementation details, backtests, or empirical data. flowchart TD A["Research Goal:<br>Review Copulas for Finance"] --> B["Key Methodology:<br>Literature Review & Analysis"] B --> C["Data/Input:<br>Financial Return Datasets<br>and Models"] C --> D["Computational Process:<br>Model Fitting &<br>Dependence Estimation"] D --> E["Key Outcomes:<br>Capturing Non-Linear Dependence<br>and Risk Assessment"]