A general technique for explicit quantile representations

Paper: arXiv 2611.06459

Authors: Wolfgang Schadner

Abstract

This work proves existence of contours independent of probability level for exact quantile integrals of strictly positive real-analytic densities. Explicit constructions cover five broad distribution families and yield a finite-interval representation of Black-Scholes implied volatility using forward functions.

Complexity vs Empirical Score

• Math Complexity: 9.0/10
• Empirical Rigor: 3.0/10
• Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper presents a highly mathematical and novel technique for explicit quantile representations using complex analysis. While the theoretical framework is robust, it lacks empirical validation or backtesting, focusing purely on the mathematical existence and construction. The methodology is clearly laid out, but the absence of empirical application limits its immediate practical rigor.

Research Flowchart

  flowchart TD
    A[Research Goal: Explicit Quantile Representations] --> B{Methodology: Existence Proofs & Constructions};
    B --> C[Inputs: Strictly Positive Real-Analytic Densities];
    C --> D{Computational Process: Exact Quantile Integrals};
    D --> E[Outcome 1: Existence of Contours Independent of Probability Level];
    D --> F[Outcome 2: Explicit Constructions for 5 Distribution Families];
    F --> G[Outcome 3: Finite-Interval Black-Scholes Implied Volatility Representation];