Status:
Professor of Applied Mathematics
Personal website:
+44 1865 615174
ORCID iD:
https://orcid.org/0000-0003-4027-5298
Research groups:
Address
University of Oxford
Andrew Wiles Building
Radcliffe Observatory Quarter
Woodstock Road
Oxford
OX2 6GG
Highlighted Publications:
A neural network based policy iteration algorithm with global H²-superlinear convergence for stochastic games on domains
Foundations of Computational Mathematics
volume N/A
page N/A-N/A
(18 May 2020)
Convergence of an Euler scheme for a hybrid stochastic-local volatility model with stochastic rates in foreign exchange markets
SIAM Journal on Financial Mathematics
issue 1
volume 9
page 127-170
(24 January 2018)
Piecewise constant policy approximations to Hamilton-Jacobi-Bellman equations
APPLIED NUMERICAL MATHEMATICS
volume 103
page 27-47
(May 2016)
Full text available
The Effect of Non-Smooth Payoffs on the Penalty Approximation of American Options
SIAM Journal on Financial Mathematics
(2013)
Penalty Methods for the Solution of Discrete HJB Equations -- Continuous Control and Obstacle Problems
SIAM Journal on Numerical Analysis
issue 50
volume 2
page 595-625
(2012)
Recent Publications:
Detecting and Repairing Arbitrage in Traded Option Prices
Applied Mathematical Finance
page 1-29
(8 February 2021)
Executive stock option exercise with full and partial information on a drift change point
SIAM Journal on Financial Mathematics
(28 October 2020)
Rectified deep neural networks overcome the curse of dimensionality for nonsmooth value functions in zero-sum games of nonlinear stiff systems
Analysis and Applications
issue 6
volume 18
page 951-999
(23 July 2020)
Probabilistic error analysis for some approximation schemes to optimal control problems
Systems and Control Letters
issue March 2020
volume 137
(10 February 2020)
Error estimates of penalty schemes for quasi-variational inequalities arising from impulse control problems
SIAM Journal on Control and Optimization
issue 1
volume 58
page 243-276
(21 January 2020)
Research interests:
Numerical analysis:
- high-dimensional PDEs
- deep neural networks
- McKean-Vlasov equations
- non-linear PDEs (in particular, of HJB-type)
- (quasi-)variational inequalities, impulse control
- multilevel and multi-index Monte Carlo
- SPDEs (in particular, of Zakai-type)
- SDEs (especially non-Lipschitz)
Mathematical and computational finance:
- derivative valuation and counterparty credit risk (in particular, large pool contagion models)
- quantification of hedging errors
- model calibration (FX, equity, credit)
- investment and incomplete markets
Preferred address:
Further details:
I am Professor of Applied Mathematics at Oxford's Mathematical Institute and Tutorial Fellow in Mathematics at St Catherine's College. I am Editor-in-Chief of The Journal of Computational Finance, and serve on the editorial board of Applied Mathematical Finance and the International Journal of Computer Mathematics.
Teaching:
I teach various Masters level courses in the areas of computational finance, numerical analysis and partial differential equations. I have examined on several Masters programmes and numerous PhD committees at and outside Oxford, and was Course Director of the professional MSc in Mathematical Finance at Oxford for over six years. I am a tutor for Applied Mathematics at St Catherine's College, Oxford, and have occasionally served as Director of Studies.
Major / recent publications:
For an up-to-date list of publications and preprints see here.