Staff Dr. Markus Holtz

Mr. Holtz is now at Baloise Group. This page is no longer maintained.

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Completed Research Projects

Adaptive and robust multigrid methods for space time discretizations

Project C2, SFB 611.

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FIDEUM: Modellierung und Bewertung von Finanzderivaten in unvollständigen Märkten

BMBF support program.

Numerical Quadrature in Finance

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Pricing of contingent claims, path- and performance-dependent options, Brownian bridge construction, principal component analysis, adaptive sparse grids, dimension reduction.

Numerische Simulation für Asset/Liability Management im Versicherungswesen

BMBF support program.

Stochastic market models and aggregation

Project Area H, Cluster of Excellence.

Valuation of Performance-Dependent Options

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Publications

  1. Dimension-wise integration of high-dimensional functions with applications to finance. M. Griebel and M. Holtz. J. Complexity, 26:455–489, 2010. Also available as INS Preprint 0809. BibTeX PDF
  2. 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. BibTeX PDF
  3. 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. BibTeX PDF
  4. 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, pages 319–341. Springer, 2008. BibTeX PDF
  5. Valuation of performance-dependent options. T. Gerstner and M. Holtz. Applied Mathematical Finance, 15(1):1–20, 2008. BibTeX PDF
  6. Sparse Grid Quadrature in High Dimensions with Applications in Finance and Insurance. M. Holtz. Dissertation, Institut für Numerische Simulation, Universität Bonn, 2008. BibTeX PDF
  7. 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. BibTeX PDF
  8. Valuation of performance-dependent options in a Black-Scholes framework. T. Gerstner, M. Holtz, and R. Korn. In J. Appleby, D. Edelman, and J. Miller, editors, Numerical Methods for Finance, 203–214. Chapman & Hall/CRC, 2007. BibTeX PDF
  9. B-spline-based monotone multigrid methods. M. Holtz and A. Kunoth. SIAM J. Numer. Anal., 45(3):1175–1199, 2007. Also as SFB 611 preprint No. 0252, 2005. BibTeX PDF
  10. Geometric tools for the valuation of performance-dependent options. T. Gerstner and M. Holtz. In M. Costantino and C.A. Brebbia, editors, Computational Finance and its Application II, 161–170. London, 2006. WIT Press. BibTeX PDF
  11. B-spline based monotone multigrid methods, with an application to the pricing of American options. M. Holtz and A. Kunoth. In P. Wesseling, C.W. Oosterlee, and P. Hemker, editors, Multigrid, Multilevel and Multiscale Methods, volume of Proc. EMG. 2005. Also as SFB 611 preprint No. 0289, 2006. BibTeX PDF
  12. Konstruktion B-Spline-basierter monotoner Mehrgitterverfahren zur Bewertung Amerikanischer Optionen. M. Holtz. Diplomarbeit, Institut für Angewandte Mathematik, Universität Bonn, Bonn, Germany, 2004. Supervised by Prof. Angela Kunoth. BibTeX PDF
  13. The computation of American option price sensitivities using a monotone multigrid method for higher order B-spline discretizations. M. Holtz. Working paper., 2004. BibTeX PDF