> geoffrey-ducournau — resume

Geoffrey Ducournau, PhD

R&D Researcher & AI Architect @ Dimtech

Research Affiliate @ Tsinghua University

Publications

// working paper · 2026

Below the Line

Detecting Accounting Anomalies in Shariah-Compliant Equities

Rémi Collin
Geoffrey Ducournau · Dimtech
Stéphane Mussard
Charles Condevaux
Jinliang Li · Tsinghua University

Sharia screening assigns listed firms a binary compliance label, computed from caps applied to reported accounting ratios. The caps are public and the label carries economic value, so a firm near a cap has an incentive to manage the inputs it reports. We propose an independent statistical plausibility check, built from public financial statements alone and applicable to any screening authority. Eight forensic detectors, covering the digit distribution, rank-size regularities, ratio dynamics, threshold proximity, cross-statement coherence, temporal consistency, sector-peer distance and cost-of-debt breaks, are mapped onto a common scale by the probability integral transform, then aggregated into composites calibrated by a non-parametric bootstrap on an authority-specific reference sample. The framework is validated across five screening regimes, in Malaysia, Indonesia, Pakistan, Saudi Arabia and the United Arab Emirates, that is 3,494 firms and 224,576 firm-quarters. On the Malaysian anchor panel, the framework flags 5.0% of ratio-compliant firm-quarters as statistically unusual; under firm-level false-discovery-rate control, the unanimity test flags 270 firms (19.9%) at q ≤ 0.01. A controlled injection study establishes a detection power of at least 89% at three standard deviations on realistic manipulation archetypes, and an end-to-end contamination study gives an area under the curve of 0.86 for digit distortions at low contamination. A flag is not proof of manipulation: it is a plausibility signal meant for a human reviewer.

Forensic AccountingAnomaly DetectionIslamic FinanceMultiple TestingFalse Discovery RateBunching
zj=Φ1 ⁣(Fj(Tj;H0^))z_j = \Phi^{-1}\!\bigl(F_j(T_j;\widehat{H_0})\bigr)

per-detector score via the probability integral transform

Z+=j=1kwjmax(zj,0),BA=Ak,ZMah2=zΣ^1z,TIUT=min1jkzjZ^{+} = \sum_{j=1}^{k} w_j\,\max(z_j,0), \quad B_{\mathcal{A}} = \frac{|\mathcal{A}|}{k}, \quad Z^{2}_{\mathrm{Mah}} = \mathbf{z}^{\top}\widehat{\Sigma}^{-1}\mathbf{z}, \quad T_{\mathrm{IUT}} = \min_{1\le j\le k} z_j

the forensic composites (spread, breadth, Mahalanobis, unanimity)

PH0(TIUT>t)=(1Φ(t))k,pIUT=(1Φ(TIUTobs))k\mathbb{P}_{H_0}\bigl(T_{\mathrm{IUT}} > t\bigr) = \bigl(1-\Phi(t)\bigr)^{k}, \qquad p_{\mathrm{IUT}} = \bigl(1-\Phi(T_{\mathrm{IUT}}^{\mathrm{obs}})\bigr)^{k}

unanimity (IUT) null distribution and p-value

This is a working paper. The full PDF is available on request — the replication code is public on GitHub.