Research

I am primarily interested in mathematical and computational finance. I have enjoyed working on free boundary problems for American options and the melting of ice, and functional expansions/occupied processes to understand the role of path dependence in finance. Broadly speaking, I am seeking out beauty in mathematical objects and financial instruments. 

PhD Dissertation

V. T.-D.  Free Boundaries, Functional Expansions, and Occupied Processes. Princeton University ProQuest Dissertations & Theses. 2024

Publications

[1] M. Shkolnikov, H. Mete Soner, and V. T.-D.  Deep Level-set Method for Stefan Problems. Journal of Computational Physics (forthcoming), 2024. Link. Preprint arXiv:2306.11601. 

[2] A. Max Reppen, H. Mete Soner, and V. T.-D.  Deep Stochastic Optimization in Finance. Digital Finance, 2022. Link

[3] V. T.-D.  Projection of Functionals and Fast Pricing of Exotic Options. SIAM Journal on Financial Mathematics, 13(2):SC74–SC86, 2022. Link

Preprints

[4] V. T.-D.  Occupied Processes: Going with the Flow. arXiv:2311.07936. 2023. In review

[5] H. Mete Soner, and V. T.-D.  Stopping Times of Boundaries: Relaxation and Continuity. arXiv:2305.09766. 2023. In review

[6] B. Dupire and V. T.-D.  Functional Expansions. arXiv:2212.13628. 2022. In review

[7] A. Max Reppen, H. Mete Soner, and V. T.-D.  Neural Optimal Stopping Boundary. arXiv:2205.04595. 2022. In review

Miscellaneous

[8] Signature, path-dependence and deep hedging. Bloomberg article, April 2022

Referee Activities

SIAM Journal on Financial Mathematics, Stochastic Processes and their Applications, SIAM Journal on Control and Optimization, Quantitative Finance, Applied Mathematical Finance, Journal of Computational Finance, Chapman and Hall / CRC, Springer