Status:
Professor of Mathematics, Fellow and Tutor in Mathematics at St John's College
+44 1865 270124
ORCID iD:
https://orcid.org/0000-0002-5686-5498
Research groups:
Address
University of Oxford
Andrew Wiles Building
Radcliffe Observatory Quarter
Woodstock Road
Oxford
OX2 6GG
Research interests:
I am a Professor of Mathematics and a member of the Mathematical and Computational Finance Group 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 have a general interest 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. My main focus is 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. These problems are intimitely linked with martingale optimal transport problem and Skorokhod embeddings. My research is supported by an ERC Starting Grant.
Further details:
My group organised a major Conference on Robust Techniques in Quantitative Finance in Oxford, 3-7 September 2018.
This follows on from a series of smaller workshop, including one on Martingale Optimal Transport in 2017, and one on Skorokhod Embeddings in 2016.
Since 2014 I gave three invited graduate courses on the Skorokhod embedding problem and its links to (robust) financial mathematics. A work-in-progress version of the lecture notes is here.
The correct spelling of my last name in LaTeX is: Ob{\l}{\'o}j
Regrettably I can not offer any student internships at the moment.
Teaching:
In 2019-2020 I am on a sabbatical research leave. I will be visiting University of Sydney, University of Technology Sydney and Monash Univeristy in Australia and University of Warsaw in Poland. I am grateful to these institutions for their hospitality. Please note that I will not check my emails regularly whilst away. I do apologise in advance if I do not respond to your message and I kindly ask you to contact me again in September 2020.
Prizes, awards, and scholarships:
International visitor, University of Sydney Mathematical Research Institute, 2019.
Recognition of Distinction, University of Oxford, 2015
ERC Starting Grant, 2013-2018.
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)
Editorial Roles:
I serve as an Associate Editor for
- Stochastic Processes and their Applications
- SIAM Journal on Financial Mathemtics
- Mathematics and Financial Economics
- Applied Mathematical Finance
Selection of videos online:
You can hear about my contributions and views on the robust approach to financial mathematics here:
Major / recent publications:
For a complete list please see the CV
- with M. Fukasawa. Efficient discretisation of stochastic differential equations, Stochastics (online first).
- with L. Carassus and J. Wiesel. The robust superreplication problem: a dynamic approach, SIAM J. Financial Math. (to appear)
- with G. Guo. Computational Methods for Martingale Optimal Transport problems, Ann. App. Probab. (to appear)
- with M. Burzoni, M. Frittelli, Z. Hou and M. Maggis. Pointwise Arbitrage Pricing Theory in Discrete Time, Math. Oper. Res. 43(3): 1034-1057, 2019.
- with X. He, S. Hu and X. Zhou. Optimal Exit Time from Casino Gambling: Strategies of Pre-Committed and Naive Gamblers. SIAM J. Control Optim. 57(3): 1845–1868, 2019.
- with X. He, S. Hu and X. Zhou. Two explicit Skorokhod embeddings for simple symmetric random walk, Stoch. Proc. App. 129(9): 3431-3445, 2019.
- with A. Aksamit, S. Deng and X. Tan. Robust pricing-hedging duality for American options in discrete time financial markets, Math. Finance 29(3): 861-897, 2019.
- with A. Cox and N. Touzi. The Root solution to the multi-marginal embedding problem: an optimal stopping and time-reveral approach, Probab. Theory Relat. Fields 173: 211-259, 2019.
- with Z. Hou. Robust pricing-hedging dualities in continuous time, Finance Stoch. 22(3): 511-567, 2018.
- with M. Beiglboeck and T. Lim. Dual attainment for the martingale transport problem, Bernoulli 25(3): 1640-1658, 2019.
- with S. Kallblad and T. Zariphopoulou. Dynamically consistent investment under model uncertainty: the robust forward criteria, Finance Stoch. 22(4): 879-918, 2018.
- with S. Nadtochiy. Robust Trading of Implied Skew, Inter. J. Theo. Appl. Fin. 20, 2017.
- with M. Davis and P. Siorpaes. Pathwise stochastic calculus with local times, Ann. Inst. H. Poincaré Probab. Statist. 54(1): 1-21, 2018.
- with X. He, S. Hu and X. Zhou. Path-Dependent and Randomized Strategies in Barberis' Casino Gambling Model, Operations Research 65(1): 97-103, 2017 (SSRN).
- with P. Spoida. An Iterated Azema-Yor Type Embedding for Finitely Many Marginals, Ann. Probab. 45(4), 2017, 2210-2247
- with C. Kardaras and E. Platen. The numeraire property and long-term growth optimality for drawdown-constrained investments, Mathematical Finance, 27(1): 68-95, 2017.
- with A. Cox and Z. Hou. Robust pricing and hedging under trading restrictions and the emergence of local martingale models, Finance and Stochastics 20(3): 669-704, 2016.
- with P. Henry-Labordere, N. Touzi and P. Spoida. The Maximum maximum of martingales with given n marginals, Ann. App. Probab., 26(1): 1-44, 2016.
- with P. Guasoni. The Incentives of Performance Fees and High Water Marks, Mathematical Finance, 26(2): 269-295, 2016. PDF
- with V. Cherny Portfolio optimisation under non-linear drawdown constraints in a semimartingale financial model, Finance & Stochastics, 17(4): 771--800, 2013. PDF
- with M. Davis and V. Raval. Arbitrage Bounds for Weighted Variance Swap Prices, Mathematical Finance 24(4): 821-854, 2013. PDF
- with L. Carraro and N. El Karoui. On Azema-Yor martingales, their optimal properties and the Bachelier-Drawdown Equation, Annals of Probability, 40(1): 372--400, 2012.
- with A.M.G. Cox. Robust pricing and hedging of double no-touch options, Finance and Stochastics, 15(3): 573--605, 2011. PDF
- Fine-tune your smile: Correction to Hagan et al. Wilmott Magazine, May 2008.
- The Skorokhod embedding problem and its offspring. Probability Surveys, 1: 321--392, 2004.
Recent pre-prints:
- with R. Lochowski, D. Promel and P. Siorpaes. Local times and Tanaka-Meyer formulae for cadlag paths, 2019.
- with S. Eckstein, G. Guo and T. Lim. Robust pricing and hedging of options on multiple assets and its numerics, 2019.
- with J. Wiesel. A unified Framework for Robust Modelling of Financial Markets in discrete time, 2018.
- with J. Wiesel. Statistical estimation of superhedging prices, 2018.
- with P. Siorpaes. Structure of martingale transports in finite dimensions, 2017.
- with A. Aksamit and Z. Hou. Robust framework for quantifying the value of information in pricing and hedging, 2016