Biography
I am a Ph.D. candidate at the Korteweg-de Vries Institute for Mathematics (KdVI) of the University of Amsterdam (UvA) and at the Grupo de Física Matemática (GFM), Instituto Superior Técnico, Universidade de Lisboa (IST-UL). My reserach focuses on stochastic analysis and optimal transport, primarily motivated by problems in mathematical finance, altough with further interests in applications to machine learning and learning theory. My work is at the intersection of probability theory, functional analysis, and partial differential equations, with a particular emphasis on stochastic differential equations, semimartingale theory, and Wasserstein geometry. I am supervised by Ana Bela Cruzeiro, Drona Kandhai, with co-supervision from Sven Karbach and Léonard Monsaingeon. Beyond academia, I run Gradient, organizing hackathons including Junction in Portugal, and is co-organizing the Portuguese Olympiads in Artificial Intelligence, Portugals' largest national competition in AI.
Research Interests
- Stochastic Analysis — stochastic differential equations, semimartingale theory, and stochastic calculus on infinite-dimensional spaces
- Optimal Transport — Wasserstein geometry, martingale optimal transport, and connections to PDEs
- Mathematical Finance — model-independent pricing, conic finance, and large financial markets
- Mathematical Machine Learning — applications of stochastic analysis and optimal transport to learning theory
Publications
- Michielon, M., Franquinho, D., Gentile, A., Khedher, A., & Spreij, P. (2024). Neural network empowered liquidity pricing in a two-price economy under conic finance settings. Quantitative Finance, 1–28.
Archive
Teaching
- Spring 2025/26 — Assistant for Econometrics (Nova SBE)
- Fall 2025/26 — Assistant for Econometrics (Nova SBE)
- Fall 2025/26 — Assistant for Mathematics for Biologists (FCUL)
- Spring 2024/25 — Assistant for Machine Learning (Nova SBE)
- Fall 2024/25 — Assistant for Computer Programming (Nova SBE)
Technical Notes
Disclaimer: These are my personal notes compiled for my own reference and learning. They may contain errors, incomplete information, or personal interpretations. While I strive for accuracy, these notes are not peer-reviewed and should not be considered authoritative sources. Please consult textbooks, research papers, or other reliable sources for academic or professional purposes.
A collection of my personal notes on various mathematical and technical topics. These are primarily for my own reference but may be useful to others.
Machine Learning
Computer Programming
Number Theory
Linear Algebra
Discrete Mathematics
Mathematical Analysis
Contact
Email: diogo.franquinho@tecnico.ulisboa.pt (IST-UL)
Email: diogo.franquinho@novasbe.pt (Nova SBE)
Office: Room 2.15, Mathematics Department, IST
Office: Office D105, NOVA SBE
If you are interested in any of the topics mentioned above, or if we seem to have common interests, feel free to reach out.