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:
ANALYSIS OF MULTI-INDEX MONTE CARLO ESTIMATORS FOR A ZAKAI SPDE
JOURNAL OF COMPUTATIONAL MATHEMATICS
issue 2
volume 36
page 202-236
(2018)
Full text available
ERROR ANALYSIS OF TRUNCATED EXPANSION SOLUTIONS TO HIGH-DIMENSIONAL PARABOLIC PDES
ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE
issue 6
volume 51
page 2435-2463
(18 December 2017)
Full text available
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
(July 2017)
Full text available
A forward equation for barrier options under the Brunick & Shreve Markovian projection
QUANTITATIVE FINANCE
issue 6
volume 16
page 827-838
(June 2016)
Full text available
Piecewise constant policy approximations to Hamilton-Jacobi-Bellman equations
APPLIED NUMERICAL MATHEMATICS
volume 103
page 27-47
(May 2016)
Full text available
Recent Publications:
Strong order 1/2 convergence of full truncation Euler approximations to the Cox-Ingersoll-Ross process
IMA Journal of Numerical Analysis
(29 October 2018)
Transition probability of Brownian motion in the octant and its application to default modelling
Applied Mathematical Finance
page 1-32
(17 June 2018)
HIGH-ORDER FILTERED SCHEMES FOR TIME-DEPENDENT SECOND ORDER HJB EQUATIONS
ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE
issue 1
volume 52
page 69-97
(15 May 2018)
Full text available
Numerical analysis of an extended structural default model with mutual liabilities and jump risk
JOURNAL OF COMPUTATIONAL SCIENCE
volume 24
page 218-231
(January 2018)
Full text available
High-order filtered schemes for time-dependent second order HJB equations
ESAIM: Mathematical Modelling and Numerical Analysis
issue 1
volume 52
page 69-97
(1 January 2018)
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.