Hello World!
Since September 2022, I have been a post-doctoral researcher in Applied Mathematics at CERMICS—École Nationale des Ponts et Chaussées (France).
In collaboration with Prof. Aurélien Alfonsi, I am currently working on stochastic Volterra equations with jumps and non-Lipschitz coefficients. Recently, we have been able to derive conditions ensuring the existence and uniqueness of a non-negative strong solution. For further information, check out our latest preprint!
I obtained my Doctor of Philosophy at LPSM—Université Paris Cité in December 2021 where I developed, under the supervision of Prof. Claudio Fontana and in collaboration with Prof. Alessandro Gnoatto, financial applications of Continuous-state Branching processes with Immigration (CBI).
I then moved to Università di Padova (Italy) where I worked from 2021 to 2022 as an assegnista di ricerca and where I concentrated upon the theoretical aspects of CBI and related processes.
Research interests
I currently demonstrate interests in the following areas of research:
- Stochastic processes.
- Stochastic differential equations.
- Stochastic Volterra equations (with jumps).
- Hawkes processes and their variants/extensions.
Publications
- Multiple yield curve modeling with CBI processes, with C. Fontana and A. Gnoatto. Mathematics and Financial Economics, 15:579–610, 2021.
- CBI-time-changed Lévy processes for multi-currency modeling, with C. Fontana and A. Gnoatto. Annals of Operations Research, 2022.
- CBI-time-changed Lévy processes, with C. Fontana and A. Gnoatto. Stochastic Processes and their Applications, 163:323–349, 2023.
Preprints
- On non-negative solutions of stochastic Volterra equations with jumps and non-Lipschitz coefficients, with A. Alfonsi. ArXiv preprint, 2024.
Presentations
- 12th European Summer School in Financial Mathematics in Padova (Italy), September 2019. Contributed talk: Multiple yield curve modeling with CBI processes.
- Brown Bag Seminar, University of Verona (Italy), October 2019. Talk: Multiple yield curve modeling with CBI processes.
- 13th European Summer School in Financial Mathematics in Vienna (Austria), September 2020. Contributed talk: CBI-time-changed processes for multi-currency modeling.
- QFW2021, XXII Workshop on Quantitative Finance in Verona (Italy), January 2021. Poster: CBI-time-changed processes for multi-currency modeling (online).
- London–Paris Bachelier Workshop in Financial Mathematics, March 2021. Poster: Multiple yield curve modeling with CBI processes (online).
- SIAM Conference on Financial Mathematics (FM21) in Philadelphia (U.S.), June 2021. Invited talk: Multiple yield curve modeling with CBI processes (online).
- 10th General AMaMeF Conference in Padova (Italy), June 2021. Contributed talk: CBI-time-changed processes for currency modeling (online).
- Seminario dottorato, Università di Padova (Italy), December 2021. Talk: Mathematical finance: a tale of stochastic processes.
- QFW2022, XXIII Workshop on Quantitative Finance in Rome (Italy), April 2022. Talk with discussion: CBI-time-changed processes for currency modeling.
- 11th World Congress of the Bachelier Finance Society in Hong Kong, June 2022. Contributed talk: CBI-time-changed processes for currency modeling (online).
- 10th International Conference on Lévy processes in Mannheim (Germany), July 2022. Contributed talk: CBI-time-changed Lévy processes.
- Groupe de Travail Méthodes Stochastiques et Finance, CERMICS–ENPC (France), November 2022. Talk: CBI-time-changed Lévy processes.
- MathRisk Conference on Numerical Methods in Finance, Udine (Italy), June 2023. Contributed talk: CBI-time-changed Lévy processes.
- Séminaire de Probabilités et Statistiques du LAMA, Université Gustave Eiffel (France), November 2023. Talk: CBI-time-changed Lévy processes.
- DCU Probability and Mathematical Finance Seminar, Dublin City University (Ireland), February 2024. Talk: On non-negative solutions of stochastic Volterra equations with jumps.
- Groupe de Travail Méthodes Stochastiques et Finance, CERMICS–ENPC (France), February 2024. Talk: On non-negative solutions of stochastic Volterra equations with jumps.
Teaching and supervision
- Tutoring of Mathematical Finance at graduate level at Univeristà di Padova (Fall 2021, 30 hours).
- Regular substitute for the Probability course at undergraduate level at CERMICS–ENPC (Fall 2022 and 2023, 6 hours each).
- Supervision of a research project at graduate level on option pricing at CERMICS–ENPC (Winter 2023).
- Introduction to Data Analysis with Python at undergraduate level at CERMICS–ENPC (Spring 2023 and Winter 2024, 10H30 each).
Reviewing
In chronological order:
- Annals of Operations Research.
- AIMS Mathematics.
- Risk–Journal of Energy Markets.
- Journal of Computational and Applied Mathematics.
- Mathematics and Computers in Simulation.
- Electronic Journal of Probability.
- Decisions in Economics and Finance.
Contact
For further information, you can reach me at guillaume.szulda(at)enpc(dot)fr