Contacting Members

Jan Hendrik Witte

Jan Hendrik Witte

Jan Hendrik Witte

Dipl.-Math.

  • DPhil Student

eMail: Jan [dot] Witte [-at-] maths [dot] ox [dot] ac [dot] uk
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Phone Number(s):

Reception/Secretary: +44 1865 273525
Direct: +44 1865 280613

Office: DH39

Departmental Address:

Mathematical Institute
24-29 St Giles'
Oxford
OX1 3LB
England

Research Interests: 

I am a third year DPhil student working in the Mathematical and Computational Finance Group, which is part of the Mathematical Institute at the University of Oxford. I have a Diplom in Mathematics from RWTH Aachen University in Germany. My research is kindly supported by the UK Engineering and Physical Sciences Research Council and by Balliol College. My supervisor is Dr Christoph Reisinger. I am a member of Balliol College as well as the Oxford-Man Institute of Quantitative Finance.

I am generally interested in numerical mathematical finance. Right now, I am looking at the numerical solution of various non-linear equations arising in finance.

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; http://arxiv.org/abs/1012.4976. To appear in SIAM Journal on Financial Mathematics.

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.

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:

Using Policy Iteration: AmericanOption_PolicyIteration.m
Using Policy Iteration combined with the Thomas Algorithm: AmericanOption_PolicyIteration_ThomasAlgorithm.m
Using a Penalty Method: AmericanOption_PenaltyScheme.m

MATLAB code for solving an incomplete market investment problem:

Using Policy Iteration: IncompleteMarket_InvestmentProblem_PolicyIteration.m
Using a Penalty Method: IncompleteMarket_InvestmentProblem_PenaltyScheme.m

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:

Using an Explicit Scheme: EarlyExercise_IncompleteMarket_ExplicitScheme.m
Using Policy Iteration: EarlyExercise_IncompleteMarket_PolicyIteration.m
Using a Penalty Method: EarlyExercise_IncompleteMarket_PenaltyScheme.m

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.
Last updated by on Tue, 22/05/2012 - 12:09pm.
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