Thomas Peyrat, PhD student at CREST-GENES and at Exiom Partners, in Finance-Insurance, has just reached a major milestone in his doctoral journey with the publication of his first paper in ESAIM: Probability and Statistics, as well as the release of a new working paper.

These two works, conducted in collaboration with his advisors Caroline Hillairet (ENSAE Paris – CREST) and Anthony Réveillac (INSA Toulouse – Toulouse Mathematics Institute), are part of his PhD carried out in partnership with Exiom Partners, a consulting firm actively involved in applied research.

🔹 A new Clark–Ocone formula for Poisson functionals
The first paper, titled A non-compensated Clark–Ocone formula for Poisson functionals, develops a decomposition formula for integrable Poisson functionals. This non-compensated version offers several technical advantages compared to the classical compensated approach, paving the way for new potential applications.
👉 Read the article in ESAIM: Probability and Statistics

🔹 Multivariate self-exciting processes with dependencies
The second work, currently available as a preprint, introduces a new class of multivariate self-exciting processes capable of modeling dependencies between event intensities and values. This modeling framework is particularly promising in insurance applications, for instance to capture links between claim frequency and severity.
👉 Read the preprint

We warmly congratulate Thomas for these important contributions, which highlight the strength of collaboration between academic research and industry, as well as the quality of doctoral training at CREST.