Track Record von Prof. Dr. Michael Griebel in Maschinellem Lernen, Computational Finance und hochdimensionaler Approximation

Patente

  • Griebel, Michael, Gerstner, Thomas, Wahl, Sebastian: Method and device for evaluation of financial derivatives using sparse grids, 2009, US7536327B2.
  • Thess, Michael; Griebel, Michael; Garcke, Jochen: Device and method for generating a classifier for automatically sorting objects, 2004, US6757584B2.

 

Projekte

Evolutionäre Selbstanpassung komplexer Produktionsprozesse und Produkte, Fraunhofer flagship project, 2019-2022, Sankt Augustin.

Research Center Machine Learning, Fraunhofer Cluster of Excellence Cognitive Internet Technologies, 2018-2020, Sankt Augustin.

Multilevel sparse tensor product approximation for manifolds and for functions and operators on manifolds, Project C04, DFG SFB 1060: Die Mathematik der emergenten Effekte, Universität Bonn, since 2013.

Likelihood-approximation for discrete choice models with sparse grids, DFG GR 1144/21-1, Universität Bonn, 2015-2018.

Stochastische Modellierung und Numerische Simulation für das Risikomanagement von Versicherungsunternehmen, Fraunhofer WISA Projekt, 2014 – 2017.

High-dimensional problems and multi-scale methods, Project Area J, Cluster of Excellence: Mathematics: Foundations, Models, Applications; Universität Bonn, 2007 – 2017.

Stochastic market models and aggregation, Project Area H, Cluster of Excellence: Mathematics: Foundations, Models, Applications, Universität Bonn, 2006 – 2017.

Lower-Dimensional Principal Manifold Learning in Higher-Dimensional Data Spaces by Sparse Grid Methods, DFG priority program 1324 „Mathematische Methoden zur Extraktion quantifizierbarer Information aus komplexen Systemen“, Universität Bonn, 2008 – 2012.

FIDEUM: Modellierung und Bewertung von Finanzderivaten in unvollständigen Märkten, BMBF support program "Mathematics for innovations in the Industrial and Service Sectors", Universität Bonn, 2007 – 2010.

Adaptive numerical valuation methods for Bermudean options, ESF Program AmaMeF – Advanced Mathematical Methods for Finance, 2005 – 2010, Universität Bonn.

Sparse grid discretizations for jump diffusion processes, ESF Program AmaMeF – Advanced Mathematical Methods for Finance, 2005 – 2010, Universität Bonn.

Numerische Simulation für Asset/Liability Management im Versicherungswesen, BMBF Support Programm „Mathematik für Innovationen“, Universität Bonn, 2004 – 2007.

Data mining with sparse grids, Cooperation with prudsys AG, Universität Bonn, 2000 – 2001.

Publikationen

Optimally rotated coordinate systems for adaptive least-squares regression on sparse grids. B. Bohn, M. Griebel, and J. Oettershagen. Accepted by SIAM International Conference on Data Mining, Calgary, 2019.

Regularized kernel-based reconstruction in generalized Besov spaces. M. Griebel, C. Rieger, and B. Zwicknagl. Foundations of Computational Mathematics, 18(2):459–508, 2018.

Error estimates for multivariate regression on discretized function spaces. B. Bohn and M. Griebel. SIAM Journal on Numerical Analysis, 55(4):1843–1866, 2017.

A representer theorem for deep kernel learning. B. Bohn, M. Griebel, and C. Rieger. Accepted. Journal of Machine Learning Research.

Note on ”The smoothing effect of integration in Rd and the ANOVA decomposition”. M. Griebel, F. Y. Kuo, and I. H. Sloan. Mathematics of Compuation, 86:1855–1876, 2017.

The ANOVA decomposition of a non-smooth function of infinitely many variables can have every term smooth. M. Griebel, F. Y. Kuo, and I. H. Sloan. Mathematics of Compuation, 86:1855–1876, 2017.

Reproducing kernel Hilbert spaces for parametric partial differential equations. M. Griebel and C. Rieger. SIAM/ASA J. Uncertainty Quantification, 5:111–137, 2017.

A sparse grid based method for generative dimensionality reduction of high-dimensional data. B. Bohn, J. Garcke, and M. Griebel. Journal of Computational Physics, 309:1–17, 2016.

Hyperbolic cross approximation in infinite dimensions. D. Dũng and M. Griebel. Journal of Complexity, 33:55–88, 2016.

On tensor product approximation of analytic functions. M. Griebel and J. Oettershagen. Journal of Approximation Theory, 207:348–379, 2016.

A sparse grid based generative topographic mapping for the dimensionality reduction of high-dimensional data. M. Griebel and A. Hullmann. In H. Bock, X. Hoang, R. Rannacher, and J. Schlöder, editors, Modeling, Simulation and Optimization of Complex Processes - HPSC 2012, 51–62. Springer International Publishing, 2014.

On a multilevel preconditioner and its condition numbers for the discretized Laplacian on full and sparse grids in higher dimensions. M. Griebel and A. Hullmann. In Singular Phenomena and Scaling in Mathematical Models, 263–296. Springer International Publishing Switzerland, 2014.

Dimensionality reduction of high-dimensional data with a nonlinear principal component aligned generative topographic mapping. M. Griebel and A. Hullmann. SIAM Journal on Scientific Computing, 36(3):A1027–A1047, 2014.

An efficient sparse grid Galerkin approach for the numerical valuation of basket options under Kou's jump-diffusion model. M. Griebel and A. Hullmann. In Sparse grids and Applications, Lecture Notes in Computational Science and Engineering, 121–150. Springer, 2013.

The smoothing effect of integration in Rd and the ANOVA decomposition. M. Griebel, F. Y. Kuo, and I. H. Sloan. Math. Comp., 82:383–400, 2013.

Fast approximation of the discrete Gauss transform in higher dimensions. M. Griebel and D. Wissel. Journal of Scientific Computing, 55(1):149–172, 2013.

An adaptive sparse grid approach for time series predictions. B. Bohn and M. Griebel. In J. Garcke and M. Griebel, editors, Sparse grids and Applications, volume 88 of Lecture Notes in Computational Science and Engineering, 1–30. Springer, 2012.

Intraday foreign exchange rate forecasting using sparse grids. J. Garcke, T. Gerstner, and M. Griebel. In J. Garcke and M. Griebel, editors, Sparse Grids and Applications, volume 88 of Lecture Notes in Computational Science and Engineering, 81–106. 2012.

Sparse grids. T. Gerstner and M. Griebel. In R. Cont, editor, Encyclopedia of Quantitative Finance. John Wiley and Sons, 2010.

Dimension-wise integration of high-dimensional functions with applications to finance. M. Griebel and M. Holtz. J. Complexity, 26:455–489, 2010.

The smoothing effect of the ANOVA decomposition. M. Griebel, F. Y. Kuo, and I. H. Sloan. J. Complexity, 26:523–551, 2010.

Principal manifold learning by sparse grids. Chr. Feuersänger and M. Griebel. Computing, Volume 85(4), 267–299, 2009.

Data Mining for the category management in the retail market. J. Garcke, M. Griebel, and M. Thess. Preprint, Institut für Numerische Simulation, Rheinische Friedrich-Wilhelms-Universität Bonn, 2009.

Data-Mining für die Angebotsoptimierung im Handel. J. Garcke, M. Griebel, and M. Thess. In M. Grötschel, K. Lucas, and V. Mehrmann, editors, Produktionsfaktor Mathematik, 111–123. acatech, Springer, Berlin, Heidelberg, 2009.

Efficient deterministic numerical simulation of stochastic asset-liability management models in life insurance. T. Gerstner, M. Griebel, and M. Holtz. Insurance: Math. Economics, 44:434–446, 2009.

A general asset-liability management model for the efficient simulation of portfolios of life insurance policies. T. Gerstner, M. Griebel, M. Holtz, R. Goschnick, and M. Haep. Insurance: Math. Economics, 42(2):704–716, 2008.

Numerical simulation for asset-liability management in life insurance. T. Gerstner, M. Griebel, M. Holtz, R. Goschnick, and M. Haep. In H.-J. Krebs and W. Jäger, editors, Mathematics – Key Technology for the Future, Part 6, 319–341. Springer, 2008.

The effective dimension of asset-liability management problems in life insurance. T. Gerstner, M. Griebel, and M. Holtz. In C. Fernandes, H. Schmidli, and N. Kolev, editors, Proc. Third Brazilian Conference on Statistical Modelling in Insurance and Finance, 148–153. 2007.

Variational problems in machine learning and their solution with finite elements. M. Hegland and M. Griebel. ANZIAM J., Volume 48, C364–C379, 2007.

Sparse grids and related approximation schemes for higher dimensional problems. M. Griebel. In L. Pardo, A. Pinkus, E. Suli, and M.J. Todd, editors, Foundations of Computational Mathematics (FoCM05), Santander, 106–161. Cambridge University Press, 2006.

Semi-supervised learning with sparse grids. J. Garcke and M. Griebel. In M.-R. Amini, O. Chapelle, and R. Ghani, editors, Proceedings of ICML, Workshop on Learning with Partially Classified Training Data, 19–28. 2005. Sparse grids. H.-J. Bungartz and M. Griebel. Acta Numerica, 13:1–123, 2004.

Dimension–adaptive tensor–product quadrature. T. Gerstner and M. Griebel. Computing, 71(1):65–87, 2003.

Classification with sparse grids using simplicial basis functions. J. Garcke and M. Griebel. Intelligent Data Analysis, 6(6):483–502, 2002. (shortened version appeared in KDD 2001, Proc. of the Seventh ACM SIGKDD, F. Provost and R. Srikant (eds.), 87-96, ACM, 2001).

Data mining with sparse grids using simplicial basis functions. J. Garcke and M. Griebel. In F. Provost and R. Srikant, editors, Proceedings of the Seventh ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, San Francisco, USA, 87–96. 2001.

On the parallelization of the sparse grid approach for data mining. J. Garcke and M. Griebel. In S. Margenov, J. Wasniewski, and P. Yalamov, editors, Large-Scale Scientific Computations, Third International Conference, LSSC 2001, Sozopol, Bulgaria, volume 2179 of Lecture Notes in Computer Science, 22–32. Springer, 2001.

Data mining with sparse grids. J. Garcke, M. Griebel, and M. Thess. Computing, 67(3):225–253, 2001.

Ausgewählte betreute Arbeiten

Error analysis of regularized and unregularized least-squares regression on discretized function spaces. B. Bohn. Dissertation, Institut für Numerische Simulation, Universität Bonn, 2017.

Construction of Optimal Cubature Algorithms with Applications to Econometrics and Uncertainty Quantification. J. Oettershagen. Dissertation, Institut für Numerische Simulation, Universität Bonn, 2017.

Intrinsic Dimension Estimation using Simplex Volumes. D. Wissel. Dissertation, Institut für Numerische Simulation, Universität Bonn, 2017.

The ANOVA decomposition and generalized sparse grid methods for the high-dimensional backward Kolmogorov equation. A. Hullmann. Dissertation, Institut für Numerische Simulation, Universität Bonn, 2015.

Sparse Grid Quadrature in High Dimensions with Applications in Finance and Insurance. M. Holtz. Dissertation, Institut für Numerische Simulation, Universität Bonn, 2008.

Maschinelles Lernen durch Funktionsrekonstruktion mit verallgemeinerten dünnen Gittern. J. Garcke. Dissertation, Institut für Numerische Simulation, Universität Bonn, 2004.

Discrete Exterior Calculus im maschinellem Lernen. A. Schier. Diploma Thesis, Institut für Numerische Simulation, Universität Bonn, 2014.

Effiziente Optimierung hochdimensionaler Probleme mit Anwendungen aus der Finanzmathematik. N. Merz. Diploma Thesis, Institut für Numerische Simulation, Universität Bonn, 2013.

Reduktion der effektiven Dimension und ihre Anwendung auf hochdimensionale Probleme. J. Oettershagen. Diploma Thesis, Institut für Numerische Simulation, Universität Bonn, 2011.

Dünngitter-Binomialbäume zur Bewertung von Multiasset-Optionen. C. Kürten. Diploma Thesis, Institut für Numerische Simulation, Universität Bonn, 2008.

Effiziente numerische Optionsbewertung in Lévy-Modellen mittels H-Matrix-Approximation. T. Osadnik. Diploma Thesis, Institut für Numerische Simulation, Universität Bonn, 2008.

Bewertung von hypotheken-basierten Wertpapieren unter Verwendung finiter Elemente. S. Paik. Diploma Thesis, Institut für Numerische Simulation, Universität Bonn, 2007.

Parameterschätzung stochastischer Prozesse aus der Finanzwelt mittels (Dünngitter-) Histogramm-Matching-Verfahren. V. Gerig. Diploma Thesis, Institut für Numerische Simulation, Universität Bonn, 2006.

Numerische Simulation von Sprung-Diffusions-Prozessen zur Optionspreisbewertung. M. Reiferscheid. Diploma Thesis, Institut für Numerische Simulation, Universität Bonn, 2006.

Numerische Verfahren zur Bewertung Bermudscher Optionen. C. Warawko. Diploma Thesis, Institut für Numerische Simulation, Universität Bonn, 2006.

Numerische Verfahren für stochastische Kontrollprobleme mit Anwendungen in der Ökonomie. A. Zulficar. Diploma Thesis, Institut für Numerische Simulation, Universität Bonn, 2006.

Optionspreisbewertung mit dünnen Gittern. T. Mertens. Diploma Thesis, Institut für Numerische Simulation, Universität Bonn, 2005.

Numerische Bewertung von Finanzderivaten durch adaptive Dünngitter–Integrationsverfahren. S. Wahl. Diploma Thesis, Institut für Angewandte Mathematik, Universität Bonn, 2001.