Prof. Mike Giles

Status

Academic Faculty

Professor of Numerical Analysis

Head of the Numerical Analysis Group

+44 1865 615291

Contact form

http://people.maths.ox.ac.uk/gilesm/

ORCID iD

https://orcid.org/0000-0002-5445-3721

Research groups

Numerical Analysis

Address

Mathematical Institute
University of Oxford
Andrew Wiles Building
Radcliffe Observatory Quarter
Woodstock Road
Oxford
OX2 6GG

Highlighted publications

Adaptive Euler-Maruyama method for SDEs with non-globally Lipschitz drift

Giles, M Fang, W Annals of Applied Probability volume 30 issue 2 526-560 (08 Jun 2020)

Multilevel nested simulation for efficient risk estimation

Giles, M Haji-Ali, A SIAM/ASA Journal on Uncertainty Quantification volume 7 issue 2 497-525 (02 May 2019)

Efficient white noise sampling and coupling for multilevel Monte Carlo
with non-nested meshes

CROCI, M GILES, M Rognes, M Farrell, P SIAM/ASA Journal on Uncertainty Quantification volume 6 issue 4 1630-1655 (20 Nov 2018)

Multilevel estimation of expected exit times and other functionals of stopped diffusions

Giles, M Bernal, F SIAM/ASA Journal on Uncertainty Quantification volume 6 issue 4 1454-1474 (18 Oct 2018)

Algorithm 955: Approximation of the inverse Poisson cumulative distribution function

Giles, M ACM Transactions on Mathematical Software volume 42 issue 1 (01 Mar 2016)

Multilevel Monte Carlo methods

Giles, M Acta Numerica volume 24 259-328 (27 Apr 2015)

Multilevel Monte Carlo Approximation of Distribution Functions and Densities

Giles, M Nagapetyan, T Ritter, K SIAM/ASA Journal on Uncertainty Quantification volume 3 issue 1 267-295 (21 Apr 2015)

Antithetic multilevel Monte Carlo estimation for multi-dimensional SDEs without Lévy area simulation

Giles, M Szpruch, L The Annals of Applied Probability volume 24 issue 4 1585-1620 (01 Aug 2014)

Further analysis of multilevel Monte Carlo methods for elliptic PDEs with random coefficients

Teckentrup, A Scheichl, R Giles, M Ullmann, E Numerische Mathematik volume 125 issue 3 569-600 (01 Nov 2013)

Multilevel Monte Carlo methods and applications to elliptic PDEs with random coefficients

Cliffe, K Giles, M Scheichl, R Teckentrup, A Computing and Visualization in Science volume 14 issue 1 3-15 (01 Jan 2011)

On the Utility of Graphics Cards to Perform Massively Parallel Simulation of Advanced Monte Carlo Methods

Lee, A Yau, C Giles, M Doucet, A Holmes, C Journal of Computational and Graphical Statistics volume 4 issue 19 769-789 (Dec 2010)

Multilevel Monte Carlo path simulation

Giles, M Operations Research volume 56 issue 3 607-617 (01 May 2008)

Research interests

In my early career, I worked at MIT and in the Oxford University Computing Laboratory on computational fluid dynamics applied to the analysis and design of gas turbines, but in around 2008 I moved into computational finance and research on Monte Carlo methods for a variety of applications.

My research focus is on improving the accuracy, efficiency and analysis of Monte Carlo methods. A particular highlight has been the development and numerical analysis of multilevel Monte Carlo methods; this has been the basis of much of my research in the past 15 years and has stimulated a lot of research elsewhere.

I am also interested in various aspects of scientific computing, including high performance parallel computing, and I have worked extensively on the exploitation of many-core GPUs for a variety of applications.

For more details please see my website.