Paper: arXiv 2310.05750

Authors: Ioannis Gasteratos, Antoine Jacquier

Abstract

We study concentration properties for laws of non-linear Gaussian functionals on metric spaces. Our focus lies on measures with non-Gaussian tail behaviour which are beyond the reach of Talagrand’s classical Transportation-Cost Inequalities (TCIs). Motivated by solutions of Rough Differential Equations and relying on a suitable contraction principle, we prove generalised TCIs for functionals that arise in the theory of regularity structures and, in particular, in the cases of rough volatility and the two-dimensional Parabolic Anderson Model. In doing so, we also extend existing results on TCIs for diffusions driven by Gaussian processes.

Complexity vs Empirical Score

  • Math Complexity: 9.5/10
  • Empirical Rigor: 1.5/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: This paper presents highly sophisticated theoretical work extending Transportation-Cost Inequalities to non-linear Gaussian functionals with applications to rough volatility and regularity structures. While mathematically rigorous and novel in its theoretical extensions, it lacks empirical backtesting or real-world financial data validation.

Research Flowchart

  flowchart TD
    A[Goal: Generalize Transportation-Cost Inequalities <br>for non-linear Gaussian functionals with non-Gaussian tails] --> B[Inputs: Rough Volatility Models & <br>2D Parabolic Anderson Model]
    B --> C[Method: Apply Contraction Principle & <br>Regularity Structures framework]
    C --> D[Computation: Derive transport bounds for <br>solutions of Rough Differential Equations]
    D --> E[Outcome 1: Extended TCIs beyond <br>classical Talagrand limits]
    D --> F[Outcome 2: New TCI bounds for diffusions <br>driven by general Gaussian processes]