Jan Hendrik Witte
 Jan Hendrik WitteDipl-Math, DPhil
eMail:
Jan [dot] Witte [-at-] maths [dot] ox [dot] ac [dot] uk
Reception/Secretary: +44 1865 273525
Mathematical Institute |
Research Interests:
From January until June 2012, I was a postdoc as part of the EPSRC Doctoral Prize scheme. From October 2008 until December 2011, I was a DPhil student in the Mathematical and Computational Finance Group, which is part of the Mathematical Institute at the University of Oxford. My research was kindly supported by the UK Engineering and Physical Sciences Research Council and by Balliol College. My supervisor was Dr Christoph Reisinger. I was a member of Balliol College as well as the Oxford-Man Institute of Quantitative Finance. My DPhil thesis can be found here. Submission in December 2011; Viva in February 2012; Final in March 2012. I have a Diplom in Mathematics from RWTH Aachen University in Germany. I am generally interested in the area of numerical mathematical finance. For further information, please see my LinkedIn profile. Major/Recent Publications:
C. Reisinger, S. D. Howison, J. H. Witte: The Effect of Non-Smooth Payoffs on the Penalty Approximation of American Options; Key Words: American Option, Jump-Diffusion Model, Penalty Method, Penalization Error, Non-Smooth Payoff; http://arxiv.org/abs/1008.0836. J. H. Witte, C. Reisinger: A Penalty Method for the Numerical Solution of Hamilton-Jacobi-Bellman (HJB) Equations in Finance, SIAM Journal on Numerical Analysis, 49(1), pp. 213-231, 2011; Key Words: HJB Equation, Numerical Solution, Penalty Method, Convergence Analysis, Viscosity Solution; Final preprint http://arxiv.org/abs/1008.0401; Final version here. J. H. Witte, C. Reisinger: A Penalty Method for the Numerical Solution of HJB Equations in Finance - Extended Abstract, AIP Conference Proceedings, 1281(1), pp. 346-349, 2010; Here. J. H. Witte, C. Reisinger: On the Use of Policy Iteration as an Easy Way of Pricing American Options; Key Words: American Option, Linear Complementarity Problem, Numerical Solution, Policy Iteration; Final preprint http://arxiv.org/abs/1012.4976; Final version here. J. H. Witte, C. Reisinger: Penalty Methods for the Solution of Discrete HJB Equations -- Continuous Control and Obstacle Problems, SIAM Journal on Numerical Analysis, 50(2), pp. 595-625, 2012; Key Words: HJB Equation, HJB Obstacle Problem, Min-Max Problem, Numerical Solution, Penalty Method, Semi-Smooth Newton Method, Viscosity Solution; Final preprint http://arxiv.org/abs/1105.5954; Final version here. L. G. Gyurko, B. Hambly, J. H. Witte: Monte Carlo Methods via a Dual Approach for some Discrete Time Stochastic Control Problems; http://arxiv.org/abs/1112.4351. J. H. Witte, D. Ples, J Corominas: The Hidden Risk Factor; Key Words: Risk Factor Analysis, Risk Premium, Currency Risk; http://ssrn.com/abstract=2158541. Further Details:
Presentation on the Numerical Solution of HJB Equations in Finance, Workshop on Quantitative Methods in Financial and Insurance Mathematics, Leiden, The Netherlands, April 2011.
MATLAB code for American option pricing:
MATLAB code for solving an incomplete market investment problem:
For further details on direct control methods in similar settings, also see the paper Numerical Methods for Controlled Hamilton-Jacobi-Bellman PDEs in Finance by P. A. Forsyth and G. Labahn. MATLAB code for pricing an early exercise contract in an incomplete market model: For further details on direct control methods in a min-max setting, also see the paper Some Convergence Results for Howard's Algorithm by O. Bokanowski, S. Maroso, and H. Zidani. |
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