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:
An adaptive Euler–Maruyama scheme for McKean–Vlasov SDEs with super-linear growth and application to the mean-field FitzHugh–Nagumo model
Journal of Computational and Applied Mathematics
volume 400
(13 July 2021)
A penalty scheme and policy iteration for nonlocal HJB variational inequalities with monotone nonlinearities
Computers and Mathematics with Applications
volume 93
page 199-213
(28 April 2021)
Calibration of local-stochastic and path-dependent volatility models to vanilla and no-touch options
Journal of Computational Finance
(26 March 2021)
Detecting and repairing arbitrage in traded option prices
Applied Mathematical Finance
issue 5
volume 27
page 345-373
(8 February 2021)
Detecting and Repairing Arbitrage in Traded Option Prices
Applied Mathematical Finance
page 1-29
(8 February 2021)
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.