Finance-Insurance
Time: 4.00 p.m.
Date:13th of May  2025
Room 3001

Antonio OCELLO (Ecole Polytechnique) “Convergence Analysis of Diffusion Models: Towards Reliable Sampling”

Abstract : Generative models are increasingly explored in insurance for tasks such as risk simulation, scenario generation, and synthetic data augmentation. Their usefulness hinges on the ability to reproduce stylized features of actuarial and claims data—such as heavy tails, skewed marginals, and rare event structures—essential for solvency analysis and pricing under uncertainty. Among the available methods, Score-Based Generative Models (SGMs), also known as diffusion models, offer a flexible framework to sample from complex, high-dimensional distributions. However, a key challenge lies in rigorously understanding their convergence.
In this talk, I will present recent advances in the theoretical analysis of SGMs, focusing on convergence guarantees relevant for actuarial applications. First, I will show how the choice of the noise schedule impacts generative performance, and provide explicit bounds on KL divergence and Wasserstein-2 distance. Second, I will introduce a new convergence analysis in Wasserstein-2 distance, based on the Ornstein–Uhlenbeck process, that remains valid beyond log-concave settings—such as for mixtures of Gaussians. Finally, I will discuss some open problems in the simulation of data for insurance purposes.
This talk is based on joint work with Stanislas Strasman, Claire Boyer, Sylvain Le Corff, and Vincent Lemaire (TMLR 2024 – https://openreview.net/forum?id=BlYIPa0Fx1), as well as a recent collaboration with Marta Gentiloni-Silveri (ICML 2025 – https://arxiv.org/pdf/2501.02298).

Organizers:  Jean-David FERMANIAN