Guillaume Szulda

Hello World!

Since September 2022, I have been a post-doctoral researcher in Applied Mathematics at CERMICSÉcole Nationale des Ponts et Chaussées (France) where I have been developing, in collaboration with Prof. Aurélien Alfonsi, a solution theory for Lévy-driven stochastic Volterra integral equations.

I obtained my Doctor of Philosophy at LPSMUniversité Paris Cité in December 2021 where I investigated, under the supervision of Prof. Claudio Fontana and in collaboration with Prof. Alessandro Gnoatto, financial applications of Continuous-state Branching processes with Immigration (henceforth CBI).

I then moved to Università di Padova (Italy) where I worked from 2021 to 2022 as an assegnista di ricerca and where I researched, alongside Prof. Claudio Fontana and Prof. Alessandro Gnoatto, the theoretical aspects of CBI-time-changed Lévy processes. 

Research interests 

Broadly speaking, my research interests have been oscillating between financial applications of stochastic processes (mostly my doctoral research) and theoretical aspects of the latter (i.e. my post-doctoral research to this day). More particularly, I currently demonstrate interests in the following more specific avenues of research:

  • Resolution of stochastic Volterra integral equations driven by Lévy-type processes.
  • Stochastic time changes, their theoretical aspects and applications to financial modeling.
  • Path-dependent stochastic equations and their applications to the modeling of equity volatility.
  • The mathematical aspects of Deep Learning and their applications to Mathematical Finance.
  • Rough Path Theory and the construction of signature-based financial models with jumps.

Publications and preprints

  1. Multiple yield curve modeling with CBI processes, with C. Fontana and A. Gnoatto, Mathematics and Financial Economics, 15:579–610, 2021.
  2. CBI-time-changed Lévy processes for multi-currency modeling, with C. Fontana and A. Gnoatto, Forthcoming in Annals of Operations Research, 2022.
  3. CBI-time-changed Lévy processes, with C. Fontana and A. Gnoatto, submitted, 2022.

Presentations

Teaching and supervision

  • Tutoring of Mathematical Finance (30 hours) at graduate level at Univeristà di Padova (2021).
  • Supervision of a research project involving master’s students on option valuation using the FFT at CERMICS–ENPC (2022–2023).
  • Regular substitute for the Probability course at undergraduate level at CERMICS–ENPC (2022–2023).

Contact

For further information, you can reach me at guillaume.szulda@enpc.fr