This is a talk presented at Nanmat conference held Nov 3-6 2026 at ICTP, Cluj.
Talk materials: 
the slides of the presentation. and here the 
Youtube video version.
Auteur : gabriel
AI4-MED: Personalized Medicine in the Era of Artificial Intelligence
Took part recently at a round table on AI in medecine within the AI4-MED conference. Several subjects were touched including the concerns, the safeguards, the trust in complex situations. More detailed reproduction of the discussion will follow on another outlet.
Deep hedging at FAAI 2025
During the FAAI 2025 conference I presented a recent work with Pierre Brugière on . See here the paper (arxiv version) and here the slides.
Executive summary: we introduce a deep-learning framework for hedging derivatives in markets with discrete trading and transaction costs, without assuming a specific stochastic model for the underlying asset. Unlike traditional approaches such as the Black–Scholes or Leland models, which rely on strong modeling assumptions and continuous-time approximations, the proposed method learns effective hedging strategies directly from data. A key contribution is its ability to perform well with very limited training data—using as few as 256 simulated price trajectories—while outperforming classical hedging schemes in numerical experiments under a geometric Brownian motion setting. This makes the approach both robust and practical for real-world applications where data and model certainty are limited.
Fake news sites: generative AI left unckecked
In a recent interview with Alexandre Boero from Clubic we discuss how recent technologies rendered possible a growing network of fake online media sites and journalists entirely generated by AI, designed to appear credible and manipulate audiences and advertisers, raising serious concerns about misinformation and the erosion of trust in digital content.
AI: The new engine of mass disinformation?
Deepfakes, AI-generated articles, fake websites mimicking the media… in a recent interview with Marie-Eve Frénay from Les Echos and we discuss the new generation of manipulative content flooding the web.
« Physics Informed Neural Networks for coupled radiation transport equations » at CM3P 2025 conference
This joint work with Laetitia LAGUZET has been presented at the 5th Computational Methods for Multi-scale, Multi-uncertainty and Multi-physics Problems Conference held in Porto, 1-4 July 2025.
Abstract Physics-Informed Neural Networks (PINNs) are a type of neural network designed to incorporate physical laws directly into their learning process. These networks can model and predict solutions for complex physical systems, even with limited or incomplete data, often using a mathematical formulation of a state equation supplemented with other information.
Introduced by Raissi et al. (2019), PINNs find applications in fields like physics, engineering, and fluid mechanics, particularly for solving partial differential equations (PDEs) and other dynamic systems. In this contribution we explore a modification of PINNs to multi-physics numerical simulation involving radiation transport equations; these equations describe the propagation of a Marshak-type wave in a temperature dependent opaque medium and is considered a good benchmark for difficult multi-regime computations.
« Transformer for Time Series: An Application to the S&P500 » at FICC 2025
This joint work with Pierre Brugière has been presented at the at the 8th Future of Information and Communication Conference 2025 held in Berlin, 28-29 April 2025.
Talk materials:
Abstract : The transformer models have been extensively used with good results in a wide area of machine learning applications including Large Language Models and image generation. Here, we inquire on the applicability of this approach to financial time series. We first describe the dataset construction for two prototypical situations: a mean reverting synthetic Ornstein-Uhlenbeck process on one hand and real S&P500 data on the other hand. Then, we present in detail the proposed Transformer architecture and finally we discuss some encouraging results. For the synthetic data we predict rather accuratly the next move, and for the S&P500 we get some interesting results related to quadratic variation and volatility prediction.
Portfolio management, risk management, statistics and dynamics of financial derivatives, M2 ISF cl+App, 2019+
Teacher: Gabriel TURINICI
Content
- classical portfolio mangement under historical probability measure: optimal portfolio, arbitrage, APT, beta
- Financial derivatives valuation and risk neutral probability measure
- Volatility trading
- Portfolio insurance: stop-loss, options, CPPI, Constant-Mix
- Hidden or exotic options: EFT, shorts
- Deep learning and portfolio strategies
Documents
NOTA BENE: All documents are copyrighted, cannot be copied, printed or ditributed in any way without prior WRITTEN consent from the author
Historical note: 2019/21 course name: « Approches déterministes et stochastiques pour la valuation d’options » + .
Statistical Learning, M1 Math 2024+
Instructor: Gabriel TURINICI
Preamble: this course is just but an introduction, in a limited amount of time, to Statistical and Machine learning. This will prepare for the next year’s courses (some of them on my www page cf. « Deep Learning » and « Reinforcement Learning »).
1/ Introduction to statistical learning : supervised, non-supervised and reinforcement learning, general learning procedure, model evaluation, under and overfitting
2/ K-nearest neighbors and the « curse of the dimensionality »
3/ Regression in high dimensions, variable selection and model regularization (ridge, lasso)
4/ Stochastic gradient descent, mini-batch
5/ Neural networks: introduction, operator, datasets, training, examples, implementations
6/ K-means clustering
Main document for the theoretical presentations: (no distribution autoried without WRITTEN consent from the author): see your « teams » group.
Exercices, implementations: see « teams » group.
Analyse numérique: évolution (M1 Math, Université Paris Dauphine – PSL, 2005-11, 2019-2025
Responsable de cours: Gabriel TURINICI
Contenu:
1 Introduction
2 EDO
3 Calcul de dérivée et contrôle
4 EDS
Bibliographie: poly distribué
Documents de support de cours, autres documents
NOTA BENE: Tous des documents sont soumis au droit d’auteur, et ne peuvent pas être distribués sauf accord préalable ÉCRIT de l’auteur.
Supports de cours: livre en anglais « Numerical simulations of time-dependent problems : applied to epidemiology, artificial intelligence and finance »
- POLY en français (mis à jour 11/03/2024). Ne pas diffuser sauf accord ÉCRIT de l’auteur. Attention: seulement les cours en amphi font foi, le poly est juste pour aider.
- poly annoté 2024/25 lors des séances de cours: cf. « teams/fichiers »
- Notes manuscrites prises lors des séances de cours 2024/25: cf « teams/fichiers »
Implementations TP:
EDO: exo sur la précision, exo stabilité , SIR(EE+H+RK4), order for the EE/H schemes/SIR
SIR (version controle, adjoint / backward); (version 2023 here)
EDS version 2025 : implémenter :
1/ simulation brownien
2/ calcul intégrale de W par/rapport à W
3/ calcul par Euler-Maruyama pour équation d’Ornstein-Uhlenbeck
4/ calcul par Euler-Maruyama faible pour modèle log-normal (Black-Scholes)
Version anciennes
2022/23:
- Autres notes manuscrites : séances de cours 2022/23 (document 1/2) , 2022/23(document 2/2) (version 2021/22 ici)
Cours du 07/03/2023 (version confinement 2021!!): video Youtube chapitre 3 (motivation calcul backward) : visioner ICI
2020/21:
- Supports de cours:
livre « Simulations numériques des problèmes dépendant du temps: appliquées à l’épidémiologie, l’intelligence artificielle et les finances« - Poly avec les annotations pendant le cours: ici.
- Notes manuscrites 2020/21 prises lors des séances de cours.
- Notes manuscrites séance de TD (groupe 1): séance 1: ICI, séance 2, séance 3, séance 4, séance 5, séance 6,séance 7 (EDS).
- Séances de TP (groupe 1) : code d’exploration de la précision, (version courte ici), code stabilité Euler explicite, code SIR (début), code contrôle SIR, code génération brownien, code Euler-Maruyama et Monte Carlo,
- Cours 1 du 19/1/2021: video Youtube chapitre 1 (motivation/EDO) : visioner ICI , ensuite revenir sur la séance Teams pour commentaires et questions.; video Youtube chapitre 1 (motivation/EDS) : visioner ICI , ensuite revenir sur la séance Teams pour commentaires et questions.; video Youtube chapitre 1 (motivation/backward) : visioner ICI , ensuite revenir sur la séance Teams pour commentaires et questions.
- Cours 2: voir le poly annoté; une video Youtube partielle chapitre 2 (EDO/existence) : visioner ICI