Professor of Scientific Computing
+44 1865 615233
University of Oxford
Andrew Wiles Building
Radcliffe Observatory Quarter
Algorithm 955: Approximation of the inverse Poisson cumulative distribution function
ACM Transactions on Mathematical Software issue 1 volume 42 (1 March 2016)
Multilevel Monte Carlo Approximation of Distribution Functions and Densities
SIAM-ASA JOURNAL ON UNCERTAINTY QUANTIFICATION issue 1 volume 3 page 267-295 (2015) Full text available
Multilevel Monte Carlo methods
Acta Numerica volume 24 page 259-328 (1 January 2015)
Trends in high-performance computing for engineering calculations
Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences issue 2022 volume 372 page 20130319- (13 August 2014)
ANTITHETIC MULTILEVEL MONTE CARLO ESTIMATION FOR MULTI-DIMENSIONAL SDES WITHOUT LEVY AREA SIMULATION
ANNALS OF APPLIED PROBABILITY issue 4 volume 24 page 1585-1620 (August 2014) Full text available
Further analysis of multilevel Monte Carlo methods for elliptic PDEs with random coefficients
Numerische Mathematik issue 3 volume 125 page 569-600 (1 November 2013)
Stochastic Finite Differences and Multilevel Monte Carlo for a Class of SPDEs in Finance
SIAM JOURNAL ON FINANCIAL MATHEMATICS issue 1 volume 3 page 572-592 (2012) Full text available
Multilevel Monte Carlo methods and applications to elliptic PDEs with random coefficients
Computing and Visualization in Science issue 1 volume 14 page 3-15 (1 January 2011)
On the Utility of Graphics Cards to Perform Massively Parallel Simulation of Advanced Monte Carlo Methods
Journal of Computational and Graphical Statistics issue 19 volume 4 page 769-789 (December 2010)
Multilevel Monte Carlo path simulation
Operations Research issue 3 volume 56 page 607-617 (1 May 2008)
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 have 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 stimulated a lot of research elsewhere.
I am also interested in various aspects of scientific computing, including high performance parallel computing, and for almost 10 years I have been working on the exploitation of GPUs (graphics processors) for a variety of financial, scientific and engineering applications.
For more details please see my webpages.
Major / Recent Publications:
M.B. Giles and P. Glasserman. `Smoking adjoints: fast Monte Carlo Greeks''. Risk, 2006.
M.B. Giles. 'Multilevel Monte Carlo path simulation'. Operations Research 56(3):607-617, 2008.
M.B. Giles. `Improved multilevel Monte Carlo convergence using the Milstein scheme', pp.343-358 in Monte Carlo and Quasi-Monte Carlo Methods 2006, Springer, 2008.
M.B. Giles and S. Ulbrich. 'Convergence of linearized and adjoint approximations for discontinuous solutions of conservation laws. Part 1: linearized approximations and linearized output functionals. Part 2: adjoint approximations and extensions. SIAM Journal of Numerical Analysis, 48(3):882-921, 2010
K.A. Cliffe, M.B. Giles, R. Scheichl, A.L. Teckentrup, 'Multilevel Monte Carlo methods and applications to elliptic PDEs with random coefficients', Computing and Visualization in Science, 14(1):3-15, 2011.
M.B. Giles, C. Reisinger. 'Stochastic finite differences and multilevel Monte Carlo for a class of SPDEs in finance', SIAM Journal of Financial Mathematics, 3(1):572-592, 2012.
A.L. Teckentrup, R. Scheichl, M.B. Giles, E. Ullmann. 'Further analysis of multilevel Monte Carlo methods for elliptic PDEs with random coefficients', Numerische Mathematik, 125(3):569-600, 2013.
M.B. Giles, L. Szpruch. 'Antithetic multilevel Monte Carlo estimation for multi-dimensional SDEs without Lévy area simulation', Annals of Applied Probability, 24(4):1585-1620, 2014
M.B. Giles. 'Multilevel Monte Carlo methods'. Acta Numerica, 24:259-328, 2015.