Professor of Scientific Computing; Oxford-Man Institute of Quantitative Finance; Associate Director, Oxford e-Research Centre
University of Oxford
Andrew Wiles Building
Radcliffe Observatory Quarter
I am Professor of Scientific Computing, a member of the Oxford-Man Institute of Quantitative Finance, and Associate Director of the Oxford e-Research Centre. I used to work 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 a new multilevel Monte Carlo approach which has stimulated a lot of research elsewhere.
I am also interested in various aspects of scientific computing, including high performance parallel computing, and in the last few years I have been working on the exploitation of graphics cards for a variety of financial, scientific and engineering applications.
For more details please see my webpage listed above.
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.