Applied Mathematics & Risk Analytics

Thomas Peyrat

Industrial PhD candidate with Exiom Partners

I work at the interface of stochastic point processes, risk analytics, and decision-making under uncertainty. My research develops MSPD-based models and tools for event-driven risks, with applications to cyber, climate, and insurance.

MSPD & Hawkes processes Cyber & emerging risks Insurance & finance

Research overview Publications CV & contact

ABOUT

Short overview of my trajectory

I am currently completing an industrial PhD in applied mathematics between ENSAE-CREST (with Caroline Hillairet), the Institut de Mathématiques de Toulouse (with Anthony Réveillac), and Exiom Partners (with Nordine Choukar). My work focuses on multivariate self-exciting point processes (MSPD), Malliavin calculus on Poisson spaces, and stress testing frameworks for emerging risks in finance and insurance.

MSPD FOR CYBER

Event-driven models and interactive toy examples

With my co-authors I build MSPD-based models to describe cyber incident dynamics and to propagate scenario-based stresses into interpretable risk indicators for insurers and decision-makers. Two interactive toy models illustrate these ideas and link multivariate self-exciting processes to stress testing and decision analytics.

Toy model #1 — Baseline MSPD dynamics

A simple multivariate self-exciting marked process for cyber events: baseline intensities, excitation kernels, and event timelines.
Open demo →

Toy model #2 — Scenario-based stress testing

MSPD shifted paths and scenario impacts on key quantities of interest (losses, exposures, KPIs), with a focus on transparency for risk and decision-making.
Open demo →

OVERVIEW

Research, teaching, and industry links

Research

My research develops theoretical tools for MSPDs using pseudo-chaotic expansions and Malliavin calculus technics. The goal is to model complex event-driven systems while keeping tractable quantities of interest for risk measurement and decision support.

Read more →

Teaching and Supervising

I have taught tutorial sessions at ENSAE, but most of my engagement with students comes through project supervision at the interface between academic modeling and practical applications. I particularly enjoy guiding students as they translate theory into real-world insights, often using industry-grade datasets and tools. My approach emphasizes an inclusive learning environment, where students feel supported, empowered, and encouraged to connect rigorous ideas with concrete data problems.

Teaching profile →

Publications

I am currently developing preprints on MSPD-based modeling for cyber and emerging risks, as well as methodological work on stress testing and sensitivities.

See publications →

Industry experience

As a consultant at Exiom Partners, I work on regulatory and risk analytics for insurance clients (Solvency II internal models, spatial climate risk, medical professional liability), bridging advanced models with real supervisory constraints.

Full CV →