University of Oxford
Andrew Wiles Building
Radcliffe Observatory Quarter
Numerical analysis, stochastic control and their applications in mathematical finance:
I am a third-year DPhil student in Mathematical and Computational Finance Group, supervised by Prof. Christoph Reisinger. My research focuses on numerically solving stochastic hybrid control problems arsing from mathematical finance. I am interested in the wellposedness of the fully nonlinear PDEs associated with these control problems, the regularity of the solutions, and efficient numerical schemes for these problems. Recently I am working on combining the classical PDE approach with the modern deep learning methodology to solve such problems in a high-dimensional setting.
Prizes, awards, and scholarships:
G-Research PhD Prize in Maths and Data Science, G-Reasearch, 2020.
Departmental Studentship, University of Oxford, 2017–2021: Full studentship covering tuition fees and living costs during the D.Phil. study.
Major / recent publications:
Christoph Reisinger and Yufei Zhang, Rectified deep neural networks overcome the curse of dimensionality for nonsmooth value functions in zero-sum games of nonlinear stiff systems, Analysis and Applications, forthcoming, 2020. [Preprint]
Kazufumi Ito, Christoph Reisinger, and Yufei Zhang, A neural network based policy iteration algorithm with global $H^2$-superlinear convergence for stochastic games on domains, Foundations of Computational Mathematics, Published online, May 2020. [Journal] [Preprint]
Christoph Reisinger and Yufei Zhang, Error estimates of penalty schemes for quasi-variational inequalities arising from impulse control problems, SIAM Journal on Control and Optimization, 58 (2020), pp. 243–276. [Journal] [Preprint]
Christoph Reisinger and Yufei Zhang, A penalty scheme for monotone systems with interconnected obstacles: convergence and error estimates, SIAM Journal of Numerical Analysis, 57 (2019), pp. 1625–1648. [Journal] [Preprint]
Roxana Dumitrescu, Christoph Reisinger, and Yufei Zhang, Approximation schemes for mixed optimal stopping and control problems with nonlinear expectations and jumps, Applied Mathematics & Optimization, Published online, July 2019. [Journal]
Xinshi Chen, Yufei Zhang, Christoph Reisinger, and Le Song, Understanding Deep Architectures with Reasoning Layer , preprint, arXiv:2006.13401, 2020. [Preprint]
Christoph Reisinger and Yufei Zhang, Regularity and stability of feedback relaxed controls, preprint, arXiv:2001.03148 [math.NA], 2020. [Preprint]
Christoph Reisinger and Yufei Zhang, A penalty scheme and policy iteration for non-local HJB variational inequalities with monotone drivers, preprint, arXiv:1805.06255 [math.NA], 2018. [Preprint]
Kazufumi Ito, Yufei Zhang, and Jun Zou, Fully discrete schemes and their analyses for forward-backward stochastic differential equations, preprint, arXiv:1804.10944 [math.NA], 2018. [Preprint]