Multilevel Monte Carlo research

Research groups

• Abo Academi (Avikainen) -- numerical analysis
• Basel (Harbrecht) -- elliptic SPDEs, sparse grids
• Bath (Scheichl, Teckentrup, Ullmann) -- elliptic SPDEs
• Duisburg (Belomestny) -- Bermudan and American options
• ETH Zürich (Barth, Lang, Schwab) -- SPDEs
• Frankfurt (Gerstner, Kloeden) -- numerical analysis
• Hong Kong (Chen) -- nested simulation in finance
• IIT Chicago (Hickernell) -- SDEs, infinite-dimensional integration, complexity analysis
• Kaiserslautern (Heinrich, Korn, Ritter) -- finance, SDEs, parametric integration, complexity analysis
• KAUST (Tempone, von Schwerin) -- adaptive time-stepping
• KTH (Szepessy) -- adaptive time-stepping
• Mannheim (Neuenkirch) -- numerical analysis
• Marburg (Dereich) -- Lévy-driven SDEs
• Munich (Hutzenthaler) -- numerical analysis
• Nottingham (Cliffe, Park) -- elliptic SPDEs
• Oxford (Giles, Reisinger, Szpruch) -- SDEs, Lévy-driven SDEs, SPDEs, numerical analysis
• Passau (Müller-Gronbach) -- infinite-dimensional integration, complexity analysis
• Princeton (Jentzen) -- numerical analysis
• Strathclyde (Higham, Mao) -- numerical analysis, exit times, stochastic chemical modelling
• WIAS (Schoenmakers) -- Bermudan and American options
• Wisconsin (Anderson) -- numerical analysis, stochastic chemical modelling

Brownian SDEs

• R. Avikainen. 'On irregular functionals of SDEs and the Euler scheme'. Finance and Stochastics, 13(3):381-401, 2009. link
• D. Belomestny, J. Schoenmakers. 'Multilevel dual approach for pricing American style derivatives'. WIAS Preprint No.1647, 2011. link
• S. Burgos, M.B. Giles. `Computing Greeks using multilevel path simulation', in Monte Carlo and Quasi-Monte Carlo Methods 2010, Springer, 2011. link
• M.B. Giles. `Multi-level Monte Carlo path simulation'. Operations Research, 56(3):607-617, 2008. link
• 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. link
• M.B. Giles, D.J. Higham, X. Mao. 'Analysing multilevel Monte Carlo for options with non-globally Lipschitz payoff'. Finance and Stochastics, 13(3):403-413, 2009. link
• M.B. Giles, B.J. Waterhouse. 'Multilevel quasi-Monte Carlo path simulation'. pp.165-181 in Advanced Financial Modelling, in Radon Series on Computational and Applied Mathematics, de Gruyter, 2009. link
• M.B. Giles. `Multilevel Monte Carlo for Basket Options'. Winter Simulation Conference 2009. link
• M.B. Giles, L. Szpruch. 'Antithetic multilevel Monte Carlo estimation for multi-dimensional SDEs without Lévy area simulation', 2012. link
• D.J. Higham, X. Mao, M. Roj, Q. Song, G. Yin. 'Mean exit times and the multi-level Monte Carlo method', 2011. link
• H. Hoel, E. von Schwerin, A. Szepessy, R. Tempone. 'Adaptive multilevel Monte Carlo simulation'. Numerical Analysis of Multiscale Computations, 82:217-234, 2012. link
• H. Hoel, E. von Schwerin, A. Szepessy, R. Tempone. 'Implementation and analysis of an adaptive multilevel Monte Carlo algorithm', 2010. link
• M. Hutzenthaler, A. Jentzen, P. Kloeden. 'Divergence of the multilevel Monte Carlo method'. link
• A. Kebaier. 'Statistical Romberg extrapolation: a new variance reduction method and applications to option pricing'. Annals of Applied Probability, 15(4):2681-2705, 2005. link
• P. Kloeden, A. Neuenkirch, R. Pavani. 'Multilevel Monte Carlo for stochastic differential equations with additive fractional noise'. 189(1):255-276, Annals of Operations Research, 2011. link
• T. Primozic. 'Estimating expected first passage times using multilevel Monte Carlo algorithm'. MSc dissertation. link

Lévy-driven SDEs

• S. Dereich. 'Multilevel Monte Carlo algorithms for Lévy-driven SDEs with Gaussian correction', Annals of Applied Probability, 21(1):283-311, 2011. link
• S. Dereich, F. Heidenreich. 'A multilevel Monte Carlo algorithm for Lévy-driven stochastic differential equations', Stochastic Processes and their Applications, 121(7):1565-1587, 2011. link
• H. Marxen. 'The Multilevel Monte Carlo method used on a Lévy driven SDE'. Monte Carlo Methods and Applications, 16(2):167-190, 2010 link
• Y. Xia, M.B. Giles. `Multilevel path simulation for jump-diffusion SDEs', in Monte Carlo and Quasi-Monte Carlo Methods 2010, Springer, 2011. link

Complexity analysis

• J. Creutzig, S. Dereich, T. Müller-Gronbach, K. Ritter. 'Infinite-dimensional quadrature and approximation of distributions', Foundations of Computational Mathematics, 9(4):391-429, 2009. link
• F.J. Hickernell, T. Müller-Gronbach, B. Niu, K. Ritter. 'Multi-level Monte Carlo algorithms for infinite-dimensional integration on ℝ^ℕ', Journal of Complexity, 26(3):229-254, 2010. link
• M. Gnewuch, 'Infinite-dimensional integration on weighted Hilbert spaces', 2010. link
• T. Müller-Gronbach, K. Ritter. 'Variable subspace sampling and multi-level algorithms', pp.131-156 in Monte Carlo and Quasi-Monte Carlo Methods 2008, Springer, 2009. link
• B. Niu, F.J. Hickernell, T. Müller-Gronbach and K. Ritter. 'Deterministic multi-level algorithms for infinite-dimensional integration on ℝ^ℕ', Journal of Complexity, 27(3-4):331-351, 2010. link

SPDEs

• A. Barth, A. Lang, C. Schwab. 'Multi-level Monte Carlo finite element method for parabolic stochastic partial differential equations', 2011. link
• A. Barth, C. Schwab, N. Zollinger. 'Multi-level Monte Carlo finite element method for elliptic PDEs with stochastic coefficients'. Numerische Mathematik, 119(1):123-161, 2011. link
• J. Charrier, R. Scheichl, A. Teckentrup. 'Finite element error analysis of elliptic PDEs with random coefficients and its application to multilevel Monte Carlo methods', 2011. link
• 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. link
• M.B. Giles. 'Multilevel Monte Carlo simulation', 2009. link
• M.B. Giles, C. Reisinger. 'Stochastic finite differences and multilevel Monte Carlo for a class of SPDEs in finance', to appear in SIAM Journal of Financial Mathematics, 2012. link
• S. Graubner. 'Multi-level Monte Carlo Methoden für stochastische partielle Differentialgleichungen', Diplomarbeit, TU Darmstadt, 2008. link
• H. Harbrecht, M. Peters, and M. Siebenmorgen. 'On multilevel quadrature for elliptic stochastic partial differential equations', Preprint 2011-01, Mathematisches Institut, Universität Basel, 2011. link
• Y.T. Hou. 'A Data-driven Stochastic Multiscale Method', 2010. link
• S. Mishra, C. Schwab, J. Sukys. 'Multi-level Monte Carlo finite volume methods for nonlinear systems of conservation laws in multi-dimensions', Journal of Computational Physics, 231(8):3365-3388, 2012. link
• A.L. Teckentrup, R. Scheichl, M.B. Giles, E. Ullmann. 'Further analysis of multilevel Monte Carlo methods for elliptic PDEs with random coefficients', preprint, 2012. link

Other applications

• D. Anderson, D.J. Higham. 'Multi-level Monte Carlo for continuous time Markov chains, with applications in biochemical kinetics', to appear in SIAM Multiscale Modelling and Simulation, 2012. link
• A. Brandt, M. Galun, D. Ron. 'Optimal multigrid algorithms for calculating thermodynamic limits', Journal of Statistical Physics, 74(1-2):313-348, 1994. link
• A. Brandt, V. Ilyin. 'Multilevel Monte Carlo methods for studying large scale phenomena in fluids', Journal of Molecular Liquids, 105(2-3):245-248, 2003. link
• S. Heinrich. 'Multilevel Monte Carlo methods', Lecture Notes in Computer Science, 2179:58-67, 2001. link
• S. Heinrich, E. Sindambiwe. 'Monte Carlo complexity of parametric integration', Journal of Complexity, 15(3):317-341, 1999. link
• D.J. Higham. 'Stochastic ordinary differential equations in applied and computational mathematics', IMA Journal of Applied Mathematics, 76(3):449-474, 2011. link
• A.L. Speight. 'A multilevel approach to control variates', Journal of Computational Finance, 12:1-25, 2009. link
• A.L. Speight. 'Multigrid techniques in economics', Operations Research, 58(4):1057-1078, 2010. link

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