Paper: arXiv 2310.09181

Abstract

Previously, in [“GR19”], we derived a rational approximation of the solution of the rough Heston fractional ODE in the special case λ= 0, which corresponds to a pure power-law kernel. In this paper we extend this solution to the general case of the Mittag-Leffler kernel with λ\geq 0. We provide numerical evidence of the convergence of the solution.

Complexity vs Empirical Score

  • Math Complexity: 9.5/10
  • Empirical Rigor: 3.0/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper is densely packed with advanced fractional calculus, asymptotic analysis, and complex integral equations, placing it firmly in high mathematical complexity. However, empirical evidence is limited to a few numerical convergence plots against a reference solver and lacks real-world data, backtests, or implementation details beyond theoretical approximations, indicating low empirical rigor.

Research Flowchart

  flowchart TD
  A["Research Goal: Generalize rational approximation of rough Heston solution"] --> B["Methodology: Derive analytical approximation for Mittag-Leffler kernel λ ≥ 0"]
  B --> C["Data/Inputs: Pure power-law kernel λ=0, Fractional ODE structure"]
  C --> D["Computational Process: Rational approximation scheme and numerical simulation"]
  D --> E["Key Finding: Validated convergence of the generalized solution"]