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:
Error analysis of truncated expansion solutions to high-dimensional parabolic PDEs
ESAIM: Mathematical Modelling and Numerical Analysis
issue 6
volume 51
page 2435-2463
(1 December 2017)
Analysis of multi-index Monte Carlo estimators for a Zakai SPDE
Journal of Computational Mathematics
issue 2
volume 36
page 202-236
(1 January 2017)
Boundary treatment and multigrid preconditioning for semi-Lagrangian schemes applied to Hamilton-Jacobi-Bellman equations
Journal of Scientific Computing
issue 1
volume 72
page 198-230
(1 January 2017)
A forward equation for barrier options under the Brunick & Shreve Markovian projection
Quantitative Finance
issue 6
volume 16
page 827-838
(2 June 2016)
Piecewise constant policy approximations to Hamilton-Jacobi-Bellman equations
APPLIED NUMERICAL MATHEMATICS
volume 103
page 27-47
(May 2016)
Full text available
Recent Publications:
Duality-based a posteriori error estimates for some approximation schemes for optimal investment problems
Computers and Mathematics with Applications
(2 January 2020)
Semi-analytical solution of a McKean–Vlasov equation with feedback through hitting a boundary
European Journal of Applied Mathematics
page 1-34
(16 December 2019)
Some regularity and convergence results for parabolic Hamilton-Jacobi-Bellman equations in bounded domains
Journal of Differential Equations
(5 December 2019)
Improved order 1/4 convergence for piecewise constant policy approximation of stochastic control problems
Electronic Communications in Probability
issue 2019
volume 24
(18 September 2019)
A penalty scheme for monotone systems with interconnected obstacles: convergence and error estimates
SIAM Journal on Numerical Analysis
issue 4
volume 57
page 1625–1648-
(9 July 2019)
Research interests:
Numerical analysis:
- high-dimensional PDEs
- non-linear PDEs (in particular, of HJB-type)
- (quasi-)variational inequalities
- multilevel and multi-index Monte Carlo
- SPDEs (in particular, of Zakai-type)
- SDEs (especially non-Lipschitz)
- McKean-Vlasov equations
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.