Mathematical and Computational Finance Members

Permanent Faculty

Dr Samuel Cohen
Research Interests: 

I am a University Research Lecturer in the Mathematical and Computational Finance Group. My main research interests are in the areas of stochastic analysis and mathematical finance. In particular, I work with Backward Stochastic Differential Equations (BSDEs), which arise in various areas in stochastic control and mathematical finance. I am interested in problems associated with decision making in the presence of risk and uncertainty.

A key problem in risk-averse decision making is time-consistency - "How can I be sure that tomorrow's decisions will satisfy today's objectives?" To guarantee time-consistency, we must ensure that the objective pursued satisfies certain properties. These properties, in general, are satisfied by solutions to BSDEs.

For more details, see my Personal Site.

Professor Mike Giles
Research Interests: 

I am Professor of Scientific Computing, a member of the Oxford-Man Institute of Quantitative Finance, and Associate Director of the Oxford e-Research Centre. I used to work at MIT and in the Oxford University Computing Laboratory on computational fluid dynamics applied to the analysis and design of gas turbines, but more recently I have moved into computational finance. 

My focus is on improving the accuracy, efficiency and analysis of Monte Carlo and finite difference methods. Recent research highlights include the use of adjoint techniques to compute sensitivities, and a new multilevel Monte Carlo method.

I am also interested in various aspects of scientific computing, including high performance parallel computing, and in the last couple of years I have been working on the exploitation of graphics cards for scientific applications in both finance and computational engineering.

For more details please see my webpage.

Major/Recent Publications: 

M.B. Giles and P. Glasserman. `Smoking adjoints: fast Monte Carlo Greeks''. Risk, 2006.

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, 2007.

M.B. Giles.  'Multilevel Monte Carlo path simulation'.  Operations Research 56(3):607-617, 2008.

M.B. Giles, D.J. Higham and X. Mao. 'Analysing multilevel Monte Carlo for options with non-globally Lipschitz payoff'. Finance and Stochastics, 13(3):403-413, 2009.

M.B. Giles. 'Vibrato Monte Carlo sensitivities', in Monte Carlo and Quasi-Monte Carlo Methods 2008, Springer, 2009.

M.B. Giles and S. Ulbrich. 'Convergence of linearized and adjoint approximations for discontinuous solutions of conservation laws.  Part 1: linearized approximations and linearized output functionals. Part 2: adjoint approximations and extensions. SIAM Journal of Numerical Analysis, 48(3):882-921, 2010

Dr Lajos Gergely Gyurko
Research Interests: 

I am a Departmental Lecturer at the Mathematical and Computational Finance Group and member of the Oxford-Man Institute of Quantitative Finance. I obtained a DPhil in Mathematics from the University of Oxford.

Currently, my research focuses on applications of Rough Paths Theory for high order approximation of solutions to stochastic differential equations, extensions of the Cubature on Wiener space framework, applications of the Multi-Level Monte Carlo methods for the numerical solution of optimal stopping problems in high dimensions and the software implementation of numerical methods.

For more details, please see my webpage.

Dr Ben Hambly
Research Interests: 

I am a University Lecturer in the Mathematical Institute. I obtained my PhD from the University of Cambridge and held post-doctoral positions at the University of Cambridge and the University of California, San Diego. I previously held academic positions at the Universities of Edinburgh and Bristol before moving to Oxford in 2000. 

My research interests are in the area of probability, stochastic processes, mathematical finance and fractals. My main interests in mathematical finance are in modelling and pricing of options. For further information see my webpage.

 

Dr Raphael Hauser
Research Interests: 

I am a member of the Numerical Analysis and Computational Finance Groups at the Mathematical Institute of the University of Oxford, and a Tutorial Fellow in Applied Mathematics at Pembroke College Oxford. Before joining Oxford as a University Lecturer, I was a postdoc at the University of Cambridge. I received my PhD in Operations Research from Cornell University in 2000. My first degree was in maths; after studying at EPFL Lausanne for the first two years, I transferred to ETH Zurich where I received a Dipl.Math ETH. 

My research interests focus on convex optimization and convex analysis. On the theory side I'm interested in complexity theory and the probabilistic analysis of algorithms, as well as in condition numbers and the design of algorithms. I also work on the theory of optimal alignments of random sequences. A large deviations approach allows to reduce many of the salient questions to convex analysis. On the applications side, I'm interested in the use of optimization models in mathematical finance, in particular in robust portfolio optimization and risk management. 

Prizes, Awards and Scholarships: 
  • Oxford University Teaching Award, 2007. 
  • 2005 SIAM Activity Group on Optimization Prize for the paper, ''The Nesterov-Todd Direction and Its Relation to Weighted Analytic Center'' (Foundations of Computational Mathematics, 1-40, 2004).
  • 2000 SIAM Student Paper Prize for the paper "Target Directions for Primal-Dual Interior-Point Methods for Self-Scaled Conic Programming''.
Major/Recent Publications: 

 

  • R.A. Hauser.  ``The S-Procedure via Dual Cone Calculus''. arXiv:1305.2444.
  • R.A. Hauser, V. Krishnamurthy and R. Tutuncu. ``Relative Robust Portfolio Optimization''. arXiv:1305.0144.
  • R.A. Hauser and H. Matzinger. ``Distribution of Aligned Letter Pairs in Optimal Alignments of Random Sequences''. arXiv: 1211.5491
  • S. Amsalu, R.A. Hauser and H. Matzinger. ``A Monte Carlo Approach to the Fluctuation Problem in Optimal Alignments of Random Strings. arXiv:1211.5489
  • F. Cucker, M. Lotz and R.A. Hauser. "Adversarial Smoothed Analysis'', J. Complexity 26 (2010), no. 3, 255–262.
  • R.A. Hauser and T. Muller. "Conditioning of random conic systems under a general family of input distributions". Foundations of Computational Mathematics 9 (2009), no. 3, 335-358. 
  • C. Durringer, R.A. Hauser and H. Matzinger. "Upper bounds on the mean curve in the LCS problem''. Stochastic Processes and their Applications 118 (2008), 629-648.

 

Teaching: 
  • Integer Programming (B22a)
  • Continuous Optimization (C12.1b)
  • Optimization in Finance (MSc in Mathematical Finance)
  • Optimization Models in Finance (Part Time MSc in Mathematical Finance) 
  • Tutorial Fellow in Applied Mathematics (Pembroke College)
Further Details: 

Current and former Postdocs:

  • Martin Lotz. Research Fellow on the DFG Grant ``Geometric Methods in the Probabilistic Analysis of Condition Numbers''. 14 Months starting from June 2008.
  • Coralia Cartis. Postdoctoral research associate on EPSRC funded project ``Stiffness in Optimisation''.

Current and former DPhil Students:

  •  Miha Troha, Numerical Analysis Group, Mathematical Institute, Oxford. September 2012 -- present. ``Optimization in Electricity Grids''.
  • Sheng Fang, Numerical Analysis Group, Mathematical Institute, Oxford. October 2010 -- present. ``Large Scale Singular Value Decompositions for Sparse Optimisation".
  • Sergey Shahverdyan, OCIAM, Mathematical Finance Group. October 2009 --present. ``Duality of Measure-Valued Optimisation and Applications to Operational Risk Management''.
  • Denis Zuev, Oxford Centre for Industrial and Applied Mathematics, jointly supervised with William Shaw (OCIAM). ``Robust Portfolio Optimisation with Structured Uncertainty''. October 2004 -- Jan 2009.
  • Nachiketa Gupta, Oxford University Computing Laboratory, jointly supevised with Neil Johnson (Physics Department). ``Constrained Kalman Filtering and Complex Systems''. October 2004 -- February 2008. 
  • Daniel Goodman, Oxford University Computing Laboratory, jointly supervised with Andrew Martin (OUCL). ``A Service Oriented Architecture and Language for Abstracted Distributed Algorithms''. October 2003 -- September 2007.
  • Jelena Nedic, Oxford University Computing Laboratory. ``On the Dynamics of Unconstrained Optimisation Methods''. October 2001 -- September 2004. 

Current and former MSc Students:

  • Fangyuan Cao, MSc in Mathematical Modelling and Scientific Computing. ``Optimal Toothbrush Design''. Sept 2013. Industrial Project sponsored by Philips.
  • Kevin Ngan, MSc in Mathematical and Computational Finance, Jun 2013. ``LCS and Data Cleaning in High Frequency Trading.''
  • Islam Hassouna, MSc in Mathematical Modelling and Scientific Computing, University of Oxford, Sept 2013. ``Flight Survey Path Optimization''. Industrial project sponsored by Arkex Ltd.
  • Naveed Ausaf, MSc in Mathematical Modelling and Scientific Computing, University of Oxford, Sept 2013. ``Optimal Sequence Alignment by Distributional Information''.
  • (Co-Supervisor of) Benjamin Timmerman, MSc in Mathematical Finance, University of Oxford, Dec 2012. ``Pricing CMS Spread Options under different Copulas''.
  • Andrew Taylor, MSc in Mathematical Modelling and Scientific Computing, University of Oxford, Sept 2012. ``Dynamic Lap Time Simulation of Circuit Racing Cars''.
  • Kishan Patel, MSc in Mathematical Modelling and Scientific Computing, University of Oxford, Sept 2012. ``Imaging with X-Ray Emitter Arrays''. Graduated with Distinction. Industrial project sponsored by Radius Diagnostics Ltd.
  • Kirat Dhillon, MSc in Mathematical Modellling and Scientific Computing, University of Oxford, Sept 2012. ``Knapsack Problems''. Industrial project sponsored by NAG Ltd.
  • Ben Wang, MSc in Mathematical Modelling and Scientific Computing, University of Oxford, Sept 2012. ``Multi-Objective Optimization''.
  • Ekta Golchha, MSc in Mathematical and Computational Finance, Jun 2012. ``Portfolio Optimization with Drawdown Constraints''.
  • Marcello Mezzedimi, MSc in Mathematical Finance, May 2011. ``Alpha Return on Portfolios Hedged with Short ETFs''.
  • Bo Guan, MSc in Mathematical and Computational Finance, Jun 2011. ``Parameter Shrinkage in Covariance Estimation''.
  • Yijun Liu, MSc in Mathematical and Computational Finance, Jun 2011. ``Optimal Trade Execution''.
  • Sally Hutchings, Mathematics and Foundations of Computer Science, Sept 2011. ``The Behaviour of Modularity-Optimizing Community Detection Algorithms''.
  • Andree Heseler, MSc in Mathematical Finance, Sept 2011. ``Asset Allocation under a Conditional Diversification Measure''.
  • Nga Hoang, MSc in Mathematical Modelling and Scientific Computing, University of Oxford. ``Parallel Line Search Methods'', 2010. Industrial project sponsored by NAG Ltd.
  • James Wood, MSc in Mathematical Modelling and Scientific Computing, University of Oxford. ``Maximum Likelihood Estimation in Phylogenic Trees'', 2010.
  • Sha Duans, MSc in Mathematical and Computational Finance, University of Oxford. ``Variable Gearing in Asset Management'', 2010.
  • Samuel Clarke, MSc in Mathematical Modelling and Scientific Computing, OUCL and OCIAM. ``Robust Staff Level Optimisation in Call Centres'', September 2007.
  • Delany Adom, MSc in Mathematical Modelling and Scientific Computing, OUCL and OCIAM. ``Robust Deviation Optimisation in Portfolio Theory'', September 2007.
  • Ivan Weber, MSc in Mathematical Modelling and Scientific Computing, OUCL and OCIAM. ``Robust Pricing in Revenue Management'', September 2005.
  • Kanika Dhyani, MSc in Mathematical Modelling and Scientific Computing, OUCL and OCIAM. ``Computational Study of a New Polynomial Time Algorithm for Linear Programming'', September 2004.
  • Christian Schroeder, MSc in Applied and Computational Mathematics, OUCL and OCIAM. ``Semidefinite Programming Bounds in Bayesian Statistics'', September 2004.
  • Quentin Decouvlaere, M.Sc.in Mathematical Modelling and Scientific Computing, OUCL and OCIAM, Oxford. ``Upper Bounds for the LCS Problem'', September 2003.
  • Berthold Heymann, part time M.Sc. in Mathematical Finance, OCIAM, Oxford.``Optimisation Approach for Asset Liability Management/Capital Allocation''. September 2004.
  • Nadine Gottschalk, part time M.Sc. in Mathematical Finance, OCIAM, Oxford. ``Robust Portfolio Management''. September 2003.
  • Roman Pausch, part time M.Sc. in Mathematical Finance, OCIAM, Oxford. ``Shortfall Risk Approach to Managing the Portfolio of a Pension Fund''. November 2002.
  • Ka Victoria Mak, M.Sc. in Mathematical Modelling and Scientific Computing, OUCL and OCIAM. ``A Heuristic for Portfolio Rebalancing with Transaction Costs'', September 2002.
  • Gauthier Lambert, M.Sc. in Mathematical Modelling and Scientific Computing, OUCL and OCIAM. ``Valuing Gas Storage'', industrial project, September 2002.
  • Juergen Stein, part time M.Sc. in Mathematical Finance, OCIAM, Oxford. ``Portfolio Theory and Market Fluctuation'', August 2002.

Current and former Undergraduate Theses Supervisees:

  • Karyn Cooke, Mathematical Institute. ``Quadratic Integer Programming and the Cross-Docking Problem'', HT 2013.
  • Maulik Pipalia, Mathematical Institute. ``Optimal Trade Execution'', HT 2012.
  • Nicholas Balz, undergraduate in Maths, Mathematical Insitute. ``Newton's Method and Newton Fractals'', Feb 2010.
  • Chris Lormoor, Oxford University Computing Laboratory. ``Large Scale Linear Programming'', June 2006. 
Professor Sam Howison
Research Interests: 

I am a University Lecturer in Applied Mathematics. I have in the past served as Director of OCIAM and of the Nomura Centre for Mathematical Finance. My research interests in physical applied mathematics include applications of differential equations. free and moving boundary problems in heat and mass transfer, and fluid dynamics. In mathematical finance, I work on derivatives pricing, asymptotic methods, models in energy markets and models for optimal production of exhaustible resources.

Recent Publications (from MathSciNet): 

More publications

Dr Hanqing Jin
Research Interests: 

I am a University Lecturer at the Mathematical Institute and a member of the Oxford-Man Institute of Quantitative Finance.  I obtained a Ph.D degree in Financial Engineering from the Chinese University of Hong Kong, and was then a postdoctoral fellow in the same university. I was an assistant professor in the National University of Singapore in September 2006--Jan 2009. 

My general interest is in Mathematical Finance, applied stochastic analysis and optimization. My work focuses on the study on portfolio selection (by stochastic control and martingale method) and optimal stopping in financial market. Recently I also worked on behavioural finance and time consistency in portfolio selection models.

Major/Recent Publications: 
1 H. Jin and X. Zhou. "Greed, leverage, and potential losses: A prospect theory perspective." Mathematical Finance 23.1: 122-142, 2013
2 Y.Hu, H. Jin, and X.Zhou, “Time-Inconsistent Stochastic Linear-Quadratic Control”,  SIAM Journal on Control and Optimization 50.3: 1548-1572, 2012
3 M. Dai, H. Jin and H. Liu, "Illiquidity, Position Limits, and Optimal Investment for Mutual Funds",  Journal of Economic Theory 146.4: 1598-1630, 2011.

4  M. Dai, H. Jin, Y. Zhong and X. Zhou, "Buy Low and Sell High", Contemporary Qunatitative Finance, edited by C. Chiarella and A. Novikov, pp. 317-334, 2010.

5 H. Jin, Z. Jin and G. Yin, "Numerical Methods for Portfolio Selection with Bounded Constraints",  Journal of Computational and Applied Mathematics, (233), pp. 564-581, 2009.

6  H. Jin and X. Zhou, “Behavioral portfolio selection in continuous time”,  Mathematical Finance, (18), pp. 385-426, 2008.

7  T. Bielecki, H. Jin, S. Pliska and X. Zhou, “Continuous-time mean--variance portfolio selection with bankruptcy prohibition”, Mathematical Finance, (15) , pp. 213-244, 2005.

Teaching: 

Stochastic Control and Dynamic Asset Allocation  (Hilary  2013),  Financial Derivatives II (Hilary 2013)

Professor Terry Lyons FLSW FRSE FRS
Research Interests: 

I am the Director (and a founding member) of the Oxford Man Institute of Quantitative Finance, and the Wallis Professor of Mathematics; previously I was the Director of the Wales Institute of Mathematical and Computational Sciences (WIMCS; 2008-2011). I came to Oxford in 2000 having previously been Professor of Mathematics at Imperial College London (1993-2000), and before that I held the Colin Maclaurin Chair at Edinburgh (1985-93).

My long-term research interests are all focused on Rough Paths, Stochastic Analysis, and applications - particularly to Finance and more generally to the summarsing of large complex data. That is to say I am interested in developing mathematical tools that can be used to effectively model and describe high dimensional systems that exhibit randomness. This involves me in a wide range of problems from pure mathematical ones to questions of efficient numerical calculation.

Recent Publications (from MathSciNet): 

More publications

Further Details: 

Stochastic analysis. This is the area of mathematics relating to the rigorous description of high-dimensional systems that have randomness. It is an area of wide-reaching importance. Virtually all areas of applied mathematics today involve considerations of randomness, and a mobile phone would not work without taking advantage of it. Those who provide fixed-rate mortgages have to take full account of it. My interests are in identifying the fundamental language and the basic results that are required to model the interaction between highly oscillatory systems where the usual calculus is inappropriate. If you google ‘Rough Paths’ and ‘Lyons’ you will find further information. My St Flour Lecture notes provide a straightforward technical introduction with all the details put as simply as possible. A more general introduction can be found in my talk/paper to the European Mathematical Society in Stockholm in 2002.
My approach is that of a pure mathematician, but my research has consequences for numerical methods, finance, sound compression and filtering. At the moment I am (speculatively) exploring their usefulness in understanding sudden shocks on dynamical systems, and also trying to understand the implications for geometric measure theory. The focus of my research directed to ‘Rough paths’ can be viewed as a successful approach to understanding certain types of non-rectifiable currents.
I actively look for applications in the mathematics I do, but my experience has led me to believe strongly in the importance of being rigorous in the development of the core mathematical ideas. For me, the word proof is synonymous with the more palatable ‘precise, convincing and detailed explanation’, and I believe it is important, even essential, to find rigorous proofs of the key mathematical intuitions so that mathematics can reliably grow and ideas can be passed on to the next generation.

Dr Michael Monoyios
Research Interests: 

I am a University Lecturer in Mathematical Finance and a Fellow of Lady Margaret Hall.

My PhD is in Theoretical Physics, from Imperial College, London. I was Royal Society Postdoctoral Fellow in Theoretical Physics at the Niels Bohr Institute, Copenhagen, 1989-90. I then traded interest rate derivatives for Security Pacific Hoare Govett, London, and returned to academia as a Research Associate in Financial Mathematics at Imperial College in 1993. I lectured Financial Mathematics at Brunel University before coming to Oxford in 2005. In 2004-2005 I held a Leverhulme Research Fellowship, and in 2005 I participated in and co-organised seminars at the Isaac Newton Institute Programme in Developments in Quantitative Finance. I was principal organiser of the workshop Further Developments in Quantitative Finance, held at the International Centre for Mathematical Sciences, Edinburgh, in July 2007.

My research focuses on applying stochastic control and filtering to optimal hedging and portfolio selection in incomplete markets, in markets with transaction costs, and to markets with partial and insider information.

Prizes, Awards and Scholarships: 

Leverhulme Research fellow, 2004-2005

Major/Recent Publications: 

Optimal exercise of an executive stock option by an insider International Journal of Theoretical and Applied Finance 14 (2011) 83-106 (With Andrew Ng);

Optimal investment with inside information and parameter uncertainty Mathematics and Financial Economics 3 (2010) 13-38 (With Albina Danilova and Andrew Ng);

Utility-based valuation and hedging of basis risk with partial information Applied Mathematical Finance 17 (2010) 519-551;

Optimal investment and hedging under partial and inside information. In Advanced Financial Modelling, H. Albrecher, W. J. Runggaldier and W. Schachermayer (eds.) Radon Series on Computational and Applied Mathematics 8 (2009) 371-410;

Utility indifference pricing with market incompleteness, in: Nonlinear Models in Mathematical Finance: New Research Trends in Option Pricing (ed. Ehrhardt M) (2008) Nova Science Publishers, Hauppage, New York;

Optimal hedging and parameter uncertainty IMA Journal of Management Mathematics 18 (2007) 331-351;

The minimal entropy measure and an Esscher transform in an incomplete market model Statistics and Probability Letters 77 (2007) 1070-1076;

Characterisation of optimal dual measures via distortion Decisions in Economics and Finance 29 (2006) 95-119;

Performance of utility-based strategies for hedging basis risk Quantitative Finance 4 (2004) 245-255;

Option pricing with transaction costs using a Markov chain approximation Journal of Economic Dynamics and Control 28 (2004) 889-913;

Efficient option pricing with transaction costs Journal of Computational Finance 7 (2003) 107-128;

Teaching: 

I teach various aspects of stochastic calculus, portfolio optimisation, and derivative valuation and hedging in incomplete markets. The specific courses include: asset pricing and portfolio theory; stochastic control and dynamic asset allocation; mathematical models of financial derivatives; I give classes on martingales through measure theory; courses I have taught in the past include: binomial models and discrete martingales; utility and portfolio theory; stochastic integration; stochastic optimisation; stochastic volatility; valuation, hedging and investment in incomplete markets. I also tutor Applied Mathematics to undergraduates at my college, Lady Margaret Hall.

Dr Jan Obloj
Research Interests: 

I am a University Lecturer at the Mathematical Institute, Fellow of St John's College and a member of the Oxford-Man Institute of Quantitative Finance. Before coming to Oxford I was a Marie Curie Post-Doctoral Fellow at Imperial College London. I hold a Ph.D. degree in Mathematics from University Paris VI and Warsaw University.

I've been focusing recently on the robust approach to Mathematical Finance, which does not start with an a priori model but rather with the information available in the markets. My general interest are in Mathematical Finance and its interplay with Probability Theory and I look at a number of different problems where tools from martingale theory and stochastic analysis can be applied. Examples include: market completion using options, volatility derivatives and extrapolation of implied volatility surface, portfolio optimisation under pathwise constraints and hedge-funds managers incentive schemes.

Prizes, Awards and Scholarships: 

Bruti-Liberati Fellow at the University of Technology Sydney, Australia, Dec 2011
Teaching Award, University of Oxford, 2010
Marie-Curie IntraEuropean Fellowship at Imperial College London, 2006-2008
French Government Co-Tutelle Scholarship, 2002-2005
(please see the CV for a full list)

Major/Recent Publications: 
(For a complete list please see the CV)
  1. with V. Cherny Portfolio optimisation under non-linear drawdown constraints in a semimartingale financial model, to appear in Finance & Stochastics
  2. with M. Davis and V. Raval. Arbitrage Bounds for Weighted Variance Swap Prices, Mathematical Finance (published online) PDF
  3. with F. Ulmer. Performance of Robust Hedges for Digital Double Barrier Options, International Journal of Theoretical and Applied Finance, 15(1): 1250003 (34 pages), 2012. PDF (preprint)
  4. with L. Carraro and N. El Karoui. On Azéma-Yor martingales, their optimal properties and the Bachelier-Drawdown Equation, Annals of Probability, 40(1): 372–400, 2012.
  5. with A.M.G. Cox. Robust pricing and hedging of double no-touch options, Finance and Stochastics, 15(3): 573–605, 2011. PDF
  6. with A.M.G. Cox. Robust hedging of double touch barrier options, SIAM Journal on Financial Mathematics, 2: 141–182, 2011. PDF
  7. with A.M.G. Cox and D. Hobson. Time homogeneous diffusion with a given marginal at a random time, ESAIM: PS, 15: 11–24, 2011. (special volume in honour of Marc Yor). PDF
  8. with M. Pistorius. On an explicit Skorokhod embedding for spectrally negative Levy processes. J. Theoret. Probab., 22(2): 418–440, 2009. PDF
  9. with Mark Davis. Market Completion using Options. in: Stettner, L. (ed). Advances in Mathematics of Finance. Banach Center Publications, 83: 49–60. Polish Academy of Sciences, Institute of Mathematics, Warsaw, 2008. PDF
  10. with A.M.G. Cox and D. Hobson. Pathwise inequalities for local time: applications to Skorokhod embeddings and optimal stopping. Ann. Appl. Probab., 18(5): 1870–1896, 2008. PDF
  11. Fine-tune your smile: Correction to Hagan et al. Wilmott Magazine, May 2008.
  12. with A.M.G. Cox. Classes of measures which can be embedded in the Simple Symmetric Random Walk. Journal of Electronic Probability, 13: 1203–1228, 2008.
  13. A complete characterization of local martingales which are functions of Brownian motion and its maximum. Bernoulli, 12: 955–969, 2006. PDF
  14. The Skorokhod embedding problem and its offspring. Probability Surveys, 1: 321–392, 2004.
Recent pre-prints:
  1. with P. Henry-Labordère, N. Touzi and P. Spoida. The Maximum maximum of martingales given marginals, 2013.
  2. with P. Spoida. An Iterated Azéma-Yor Type Embedding for Finitely Many Marginals, 2013
  3. with C. Kardaras and E. Platen. The numeraire property and long-term growth optimality for drawdown-constrained investments, 2012
  4. with A.M.G. Cox and D. Hobson. Utility theory front to back - inferring utility from agents' choices, 2011.
  5. with P. Guasoni. The Incentives of Performance Fees and High Water Marks, 2010.
Teaching: 

I am currently on sabbatical leave.

Further Details: 

In August 2012 I gave a lecture course during the 5th European Summer School in Financial Mathematics. Introductory slides for the course are available here while a work-in-progress version of the notes is here.

In March 2010, I organised the first Robust Methods in Quantitative Finance Conference at the Oxford-Man Institute.

The correct spelling of my last name in LaTeX is: Ob{\l}{\'o}j

Regratably I can not offer any student interships at the moment.

Locations of Site Visitors

Dr Christoph Reisinger
Research Interests: 

I am a University Lecturer in Mathematical Finance and Tutorial Fellow in Mathematics at St Catherine's College. My doctorate from the University of Heidelberg is in scientific computing, my first degree from Linz in applied mathematics.

Current research includes, mathematically, the numerical analysis of high-dimensional PDEs, non-linear PDEs and variational inequalities, simulation of SPDEs, Bayesian techniques for parameter estimation problems. Application areas include the pricing of equity and credit basket derivatives, calibration of financial instruments, early-exercise options and valuation and investment in incomplete markets

Major/Recent Publications: 

J.H. Witte, C. Reisinger, A Penalty Method for the Numerical Solution of Hamilton-Jacobi-Bellman (HJB) Equations in Finance, SIAM Journal of Numerical Analysis, 49(1), pp213--231, 2011. [Link to preprint version.]

N. Bush, B.M. Hambly, H. Haworth, L. Jin, C. Reisinger, Stochastic Evolution Equations in Portfolio Credit Modelling, SIAM Journal on Financial Mathematics, 2(1), 627--664, 2011. [Link to preprint version with applications to exotic credit products.]

H. Haworth, C. Reisinger, W. Shaw: Modelling Bonds and Credit Default Swaps
Using a Structural Model with Contagion, Quantitative Finance (2008).

C. Reisinger, G. Wittum: Efficient Hierarchical Approximation of High-Dimensional Option Pricing Problems, SIAM Journal on Scientific Computing (2007).

Professor Xun Yu Zhou
Research Interests: 

I am the Nomura Chair of Mathematical Finance and Director of the Nomura Centre for Mathematical Finance. Prior to joining Oxford I was Chair of Systems Engineering and Engineering Management at Chinese University of Hong Kong. I am a Fellow of IEEE and a winner of the SIAM Outstanding Paper Prize. I obtained Ph.D. in Fudan University in 1989, and have worked in Kobe University and University of Toronto.

My general research interests are in quantitative finance, stochastic control, and applied probability, while I am recently engaged in the mathematical behavioral finance research.

For more information please visit my webpage.

Postdoctoral Research Assistants

Affiliate Researchers

Dr Vicky Henderson
Research Interests: 

I am a Senior Research Fellow at the Oxford-Man Institute for Quantitative Finance, a member of the Mathematical and Computational Finance Group and Oriel College. I hold a PhD in Mathematics from the University of Bath, and following this, held postdoctoral positions at ETH Zurich, University of Warwick, and a Nomura Research Fellowship at Oxford. I spent three years as an Assistant Professor at Princeton University and two years as a Reader at University of Warwick before returning to Oxford in September 2008.

My research interests include optimal stopping and optimal control problems, with applications to real options, executive stock options, and recently, behavioural finance. I have worked for several years on utility indifference pricing, in particular, approximate prices via expansions under CRRA, and more recently, horizon-unbiased utilities and associated optimal stopping problems. My earlier research interests include stochastic volatility models, and exotic options, particularly passport options and asian options.

For further details please see my website at the Oxford-Man Institute.

Further Details: 

Dr Gechun Liang
Research Interests: 

I am a Postdoctoral Research Fellow at the Oxford-Man Institute of Quantitative Finance, starting from Michaelmas Term 2010. Prior to that, I was a student member of the Oxford-Man Institute, whilst completing my D.Phil. (Ph.D.) in Mathematics at the Mathematical Institute under the supervision of Professor Terry Lyons and Dr Zhongmin Qian.

My research interests are mainly focused on mathematical finance and stochastic analysis. I am especially interested in backward stochastic differential equations (BSDEs), rough path theory, optimal investment and credit risk modeling and management.

Major/Recent Publications: 
  • A multi-period bank-run model for liquidity risk (with Eva Lütkebohmert and Yajun Xiao), Review of Finance, accepted.
  • The backward stochastic dynamics on a filtered probability space (with Terry Lyons and Zhongmin Qian), Annals of Probability, Vol.39, No.4, (2011), 1422-1448.
  • A modified structural model for credit risk (with Lishang Jiang), IMA Journal of Management Mathematics, Vol.23, No.2, (2012), 147-170.
  • The valuation of the basket CDSs in a primary-subsidiary model (with Jianwei Lin, Sen Wu and Harry Zheng), Asia-Pacific Journal of Operational Research, Vol.28, No.2, (2011), 213-238.
  • The credit risk and pricing of OTC options (with Xuemin Ren), Asia-Pacific Financial Markets, Vol.14, No.1, (2007), 45-68.

Working Papers:

  • A continuous time structural model for insolvency, recovery and rollover risks (with Eva Lütkebohmert and Wei Wei), arXiv:1209.3513v1.
  • Fully coupled forward-backward stochastic dynamics and functional differential systems (with Matteo Casserini), arXiv:1112.4978v1.
  • A multidimensional exponential utility indifference pricing model with applications to counterparty risk (with Vicky Henderson), arXiv:1111.3856v1.
  • A functional approach to FBSDEs and its application in optimal portfolios (with Terry Lyons and Zhongmin Qian), arXiv:1011.4499v1.
  • Pseudo linear pricing rule for utility indifference valuation (with Vicky Henderson), Revised and resubmitted.

Teaching: 

Tutor and Teaching Assistant for the following courses: Stochastic Differential Equations, Applied Partial Differential Equations, Mathematical Models of Financial Derivatives, Financial Derivatives, etc.

Visitors

 Ferhana Ahmad
Research Interests: 

I am a DPhil student in Mathematical and Computational Finance group which is a part of Mathematical Institute at University of Oxford. I have a Masters degree in Mathematical and Computational Finance from University of Oxford. I also have a BS(Mathematics) from COMSATS Institute of Information Technology, Pakistan. I am a member of Lady Margaret Hall and an associate member of Oxford-Man Institute of Quantitative Finance.

I am working on mortgage backed securities with Dr. Ben Hambly. I worked on the techniques of modelling and pricing these securities in a structural framework for large portfolios. This involves proving the existence and uniqueness of resulting stochastic partial differential equations, solving them numerically and estimating the parameters using market data through calibration. 

Prizes, Awards and Scholarships: 

Associate member of Oxford-Man Institute (July 2010/--)

Teaching: 
TA: MScMCF, Financial Derivatives MT 2008

TA: MScMCF, Stochastic Calculus and Fixed Income Markets HT 2009

Tutor: MScMCF, Financial Derivatives MT 2009

Tutor: MScMCF, Stochastic Calculus and Fixed Income Markets HT 2010

Tutor: MScMCF, Practical Stochastic Calculus/Asset Pricing MT 2010

Demonstrator: Mathematics with MuPad MT 2010/--

Further Details: 

Member of the Consultative Committee for Graduates (CCG) 2010/2011

Student representative on Mathematical Institute Buildings Committee 2010/2011

Student representative on the MPLS Divisional Graduate Joint Consultative Forum 2011/2012

 Alok Gupta
Research Interests: 

I worked in the Mathematical and Computational Finance Group which is part of the Mathematical Institute at the University of Oxford. I completed my BA degree in Mathematics at the University of Cambridge and my MSc in Mathematics & Finance at Imperial College, London. I recently completed my PhD research in Mathematical Finance. The PhD was funded by a CASE Award made jointly between the UK Engineering and Physical Sciences Research Council and Nomura Bank. My PhD supervisor was Dr Christoph Reisinger and I was a Senior Scholar at Hertford College.

I completed a 6 month Post-Doctorate Scholarship as part of the PhD-Plus scheme piloted by the UK Engineering and Physical Sciences Research Council (EPSRC). I then held a Nomura Postdoctorate at the Mathematical Instutute at the University of Oxford in conjuction with a Junior Research Fellowship at Wadham College. I am now an Academic Visitor in Mathematical Finance at Oxford University.

In my research I consider a Bayesian approach to calibrating non-parametric financial models. This enables computation of a distribution of prices for financial derivatives and hence some measure of the model uncertainty in the prices and risk. In addition I have developed analytic consistency properties for Bayesian estimators and designed optimal Bayesian hedging strategies.

Further details regarding my research interests and other academic matters can be found at my homepage.

Prizes, Awards and Scholarships: 

My full CV is available on request.

Further Details: 

Research Students

 Bahman Angoshtari
Research Interests: 

I am a fourth year D.Phil. student in Mathematical and Computational Finance Group, and a student member of Oxford-Man Institute of Quantitative Finance. My research, supervised by Prof. T. Zariphopoulou, lies on the interaction between Portfolio Choice Theory and Financial Econometrics. Currently, my focus is on dynamic asset allocation models in cointegrated markets, with applications including pairs/spread trading and statistical arbitrage techniques.

 Ian J. Angus
Research Interests: 

I am a second year DPhil student in Mathematical and Computational Finance.  I completed my MMath degree in Mathematics and Statistics at the University of Oxford.  I am supervised by Dr Michael Monoyios and I am a member of St Anne's College.  My research funding is provided by the UK Engineering and Physical Sciences Research Council.

My research interests include optimal portfolio selection over finite and infinite horizons using primal and dual methods of utility maximisation, maturity-independent and dynamic utility functions, and applications to pricing real options, stochastic income streams and American options.

 Karolina Bujok
Research Interests: 

I am a forth year DPhil student working in the Mathematical and Computational Finance Group. I have a Masters degree in Financial Mathematics from King's College London (2008) and a Masters degree in Quantitative Methods in Economics and Information Systems from Warsaw School of Economics (2005).  I am currently working on developing efficient numerical methods to price basket credit derivatives via structural models. My supervisor is Dr. Christoph Reisinger.

Prizes, Awards and Scholarships: 

Oxford-Man Institute of Quantitative Finance Scholarship 2011/2012

St Catherine's College Scholarship (Alan Taylor) 2010/2011

CASE award funded jointly by EPSRC and Nomura 2008/2011

King's College London Prize for the Best Overall Performance in MSc Financial Mathematics 2008

Major/Recent Publications: 

K. Bujok, C. Reisinger, Numerical Valuation of Basket Credit Derivatives in Structural Jump-Diffusion Models, Journal of Computational Finance, accepted.


 Sylvestre Burgos
Research Interests: 

I am a third year DPhil student at the Mathematical and Computational Finance Group/Oxford-Man Institute of Quantitative Finance. I hold a BSc in Mathematics (Universite Pierre & Marie Curie - Paris 6), a Diplome d'Ingenieur (MSc in Engineering - Ecole Centrale Paris) as well as an MSc in Mathematical and Computational Finance (University of Oxford). I am a member of the Oxford-Man Institute of Quantitative Finance. My Supervisor is Prof Mike Giles and I am a scholar of Lady Margaret Hall.

My research focuses on improving Monte Carlo methods. I am currently working on the recent Vibrato and Multilevel Monte Carlo techniques and their use for the computation of Greeks.

Prizes, Awards and Scholarships: 

Oxford-Man Institute of Quantitative Finance Scholarship 2011-2012

Oxford-Man Institute of Quantitative Finance Scholarship 2010-2011

Lady Margaret Hall Divisional Scholarship 2009-2010

Lady Margaret Hall scholarship for the best candidate in the Mathematical Physical and Life Sciences Division 2008-2009

Major/Recent Publications: 

"Computing Greeks using multilevel path simulation" in Monte Carlo and Quasi Monte Carlo Methods 2010, Springer Verlag, late 2011

Teaching: 

Supervisor: Structured Projects in Mathematical Modelling and Numerical Computation, Part B, 2011-2012

Class tutor: Numerical Methods, MSc MCF, 2011-2012

Supervisor: Structured Projects in Mathematical Modelling and Numerical Computation, Part B, 2010-2011

Class tutor: Numerical Methods, MSc MCF, 2010-2011

Class tutor: Introduction to probability, MSc MCF, 2010

TA: Numerical Methods, MSc MCF  2009 - 2010

 Vladimir Cherny
Research Interests: 

I am a third year DPhil student at the Mathematical and Computational Finance Group. I hold a Specialist Diploma in Mathematics (Moscow State University). I am working under the supervision of Dr. Jan Obloj.

I am currently working on portfolio optimization problems with pathwise constraints.

Major/Recent Publications: 

with Dr. Jan Obloj  "Portfolio optimisation under non-linear drawdown constraints in a semimartingale financial model",  2011, Preprint

Teaching: 

Teaching Assistant for

B10b Mathematical Models of Financial Derivatives (HT'10, HT'11)

MSc MCF Financial Derivatives II (HT'10, HT'11)

B4a Banach Spaces (MT'09) 

Tutor for

MSc MCF Financial Derivatives II (HT'12)

 Alice Dub
Research Interests: 

I am a second year DPhil student working in the Mathematical and Computational Finance Group and an associate member of the MAN Institute of Quantitative finance. I hold a Diplom in Mathematics and Business Studies from Ludwig- Maximulians University in Munich as well as an MSc in Mathematics fromUniversity of St Andrews. My Supervisor is Dr Ben Hambly and I am a member of St Anne's College.

Currently I am looking at the Merton Problem of optimal investement with intermediate consumptions. Here I am cosidering perturbations to the well known model. In addition l want to look at similar setups but with non-linear weath dynamics trying to find optimal portfolio and consumption quantities for general as well as particularly chosen utility functions.

 Sigrid Kallblad
Research Interests: 

I'm a second year DPhil student in the Mathematical and Computational Finance Group and a member of Lady Margaret Hall.

I'm supervised by Prof T Zariphopoulou and my research interests are in stochastic control and portfolio optimisation.

 Sergey Shahverdyan
Research Interests: 

I am a third year DPhil student at the Mathematical and Computational Finance Group. I have a Masters degree in Mathematical and Computational Finance from University of Oxford. I also have a BS(Applied Mathematics) from Yerevan State University, Armenia.

My supervisor is Dr Raphael Hauser and I am working on optimisation methods in Operational Risk management, optimisation problems over measure spaces.

Teaching: 

TA: Integer Programming, MT 2009,2010

TA: MScMCF, Practical Stochastic Calculus/Asset Pricing MT 2009, 2010

TA: MScMCF, Fixed Income Markets HT 2011

 Peter Spoida
Research Interests: 

I am a second year DPhil student in Mathematical and Computational Finance group.

My research interests lie in probability theory and its interplay with Mathematical Finance. Together with Jan Obłoj I try to develop the robust pricing and hedging framework further to allow for more flexible incorporation of both, market and statistical information. In particular, we try to incorporate statistical confidence intervals on total realised volatility and understand the consequences for pricing, pathwise hedging and forms of arbitrage. Key mathematical tool for doing this include optimality properties of solutions to the Skorokhod embedding problem and pathwise stochastic calculus.

Prizes, Awards and Scholarships: 

Student Membership at the Oxford-Man Institute of Quantitative Finance.

Major/Recent Publications: 

with Pierre Henry-Labordere, Jan Obloj and Nizar Touzi, Maximum Maximum of Martingales given Marginals, http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2031461

with Jan Obloj, An Interated Azema-Yor Type Embedding for Finitely Many Marginals, http://arxiv.org/abs/1304.0368

Teaching: 

TA: MScMCF, Financial Derivatives 2, HT 2012

TA: MScMCF, Practical Stochastic Calculus and Asset Allocation, MT 2012

Tutor: MScMCF, Fixed Income Markets, HT 2013

Further Details: 

I am a member of Lady Margaret Hall.

 Pedro Vitoria
Research Interests: 

I am a first year DPhil student at the Mathematical and Computational Finance Group under Prof. Thaleia Zariphopoulou. I'm also a member of the Stochastic Analysis Group and Magdalen College.

My research interests are in the areas of Stochastic Analysis, Optimal Control and Mathematical Finance. My current focus is in Portfolio Optimisation, in particular in Forward Utility.

 Rasmus Wissmann
Research Interests: 

I am a third year DPhil student in the Mathematical and Computational Finance Group at the Mathematical Institute. Previously I completed a MSc in Computer Science from the University of Oxford and a BSc in Mathematics from the Technical University Munich. My current work is kindly supported by EPSRC and Nomura.

I am interested in numerical and computational mathematical finance. My current research focuses on numerical PDE and MC methods for high-dimensional problems. My DPhil supervisor is Dr. Christoph Reisinger. 

Major/Recent Publications: 

Numerical Valuation of Bermudan and Path-Dependent Interest Rate Derivatives via PDE Expansions, Christoph Reisinger and Rasmus Wissmann, Preprint

 Yuan Xia
Research Interests: 

I am a third year DPhil student at the Mathematical and Computational Finance Group and also a member of the Oxford-Man Institute of Quantitative Finance. I hold a BSc in Mathematics (Peking University). My Supervisor is Prof Mike Giles.

My research interests include Monte Carlo methods. Currently, I am working on Multilevel Monte Carlo method for jump-diffusion and more general processes.

Other Staff

 Daniel Jones
Teaching: 

DPhil and MSc thesis supervisor

Lecturer, MSc in Mathematical and Computational Finance (full-time course)

Lecturer, MSc in Mathematical Finance (part-time course)

Further Details: 

I am a partner at Quadrature Capital LLP, a new quantitative trading firm, and continue to be actively involved in teaching and research at the Institute.

 Jan Hendrik Witte
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:

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.