Convergence bounds for the pricing approximations

Establish convergence bounds for the Hartree closure, the conditional-CEV reduction, and the displacement booster used in the Dyson–Schwinger pricing framework.

Background

The paper validates its numerical pricing methods against synthetic benchmarks but explicitly distinguishes empirical accuracy from analytical guarantees. In particular, the Hartree closure, the conditional-CEV reduction, and the displacement booster are used as approximation components, and their convergence behavior is not analytically bounded. Establishing such bounds would provide rigorous control over the approximation error and substantiate the claim that the framework is systematically improvable.

References

Correctness here is established numerically rather than analytically: we prove no convergence bounds for the Hartree closure, the conditional-CEV reduction or the displacement booster, and the ``systematically improvable'' claim is empirical except where a diagram order is added explicitly.

— Dyson-Schwinger Effective-Action Methods for Rough Volatility: A Correlation-Response Architecture for Calibration, Exotics and Risk  (2609.37741 - Pauquay, 29 Sep 2026) in Section 7, Limitations and Outlook