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Photo of Mike Giles

Prof. Mike Giles

Status
Academic Faculty

Professor of Scientific Computing

@email

Contact form
http://people.maths.ox.ac.uk/gilesm/
+44 1865 615291
ORCID iD
https://orcid.org/0000-0002-5445-3721
Research groups
  • Mathematical and Computational Finance
  • 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 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)
Multilevel Monte Carlo methods
Giles, M Acta Numerica volume 24 259-328 (01 Jan 2015)
ANTITHETIC MULTILEVEL MONTE CARLO ESTIMATION FOR MULTI-DIMENSIONAL SDES WITHOUT LEVY AREA SIMULATION
Giles, M Szpruch, L ANNALS OF APPLIED PROBABILITY volume 24 issue 4 1585-1620 (Aug 2014) http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000338270800008&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=4fd6f7d59a501f9b8bac2be37914c43e
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 more recently 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. Related to this, I am now researching low and mixed-precision computing, including stochastic rounding error analysis.

For more details please see my website.

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