From a Hierarchy of Stochastic Differential Equations to a Hierarchy of Generalized Beta Distributions

Battle Count: 50

Highly relevant for modeling asset returns, wealth distributions, and stochastic volatility. The distinction between dynamical and distributional generalizations offers new ways to model tail risks and support structures in financial data, though it is a theoretical contribution rather than a direct trading strategy.

Implementing the PDFs and CDFs requires handling special functions (Appell F1, Hypergeometric 2F1, Incomplete Beta/Gamma functions) and careful parameter mapping. The theoretical derivation is complex, but the resulting formulas are provided in tables.

The paper provides full analytical derivations, closed-form PDFs/CDFs, and parameter mappings in the appendices (Tables A.1-A.6). No code is provided, but the mathematical framework is self-contained and reproducible via symbolic computation.