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 work in the Mathematical and Computational Finance and Stochastic Analysis research groups at the Mathematical Institute, am 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 Statistics. My main focus is on robust approach to Mathematical Finance and data-driven paradigm in modelling and optimisation. The ensuing problems are often interdisciplinary. In particular, I am currently involved with (martingale) optimal transport theory, both its theory and numerical methods.
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:
I teach both undergraduate and graduate material.
This year, I taught third year undergradaute course B8.1 Probability, Measure and Martingales and two courses on the MSc in Mathematical and Computational Finance: Quantitative Risk Management and Market Microstructure and Algorithmic Trading.
I am currently the Chair of Honour School of Mathematics Part A Examiners.
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
- Finance and Stochastics
- Stochastic Processes and their Applications
- SIAM Journal on Financial Mathemtics
- Mathematics and Financial Economics
- Applied Mathematical Finance
I am a guest editor at the Mathematical Finance co-editing with Thaleia Zariphopoulou a special volume dediacted to the memory of Mark H.A. Davis.
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 S. Eckstein, G. Guo and T. Lim. Robust pricing and hedging of options on multiple assets and its numerics, SIAM J Financial Math. 12(1): 158-188, 2021.
- with J. Wiesel. A unified Framework for Robust Modelling of Financial Markets in discrete time, Finance Stoch, online, 2021.
- with J. Wiesel. Robust estimation of superhedging prices, Ann. Stat. 49(1): 508-530, 2021.
- with A. Aksamit and Z. Hou. Robust framework for quantifying the value of information in pricing and hedging, SIAM J. Financial Math. 11(1): 27-59, 2020.
- 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. 10(4): 907–941, 2019.
- with G. Guo. Computational Methods for Martingale Optimal Transport problems, Ann. App. Probab. 29(6): 3311-3347, 2019.
- 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 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 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 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 Stoch, 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 Stoch, 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 D. Bartl, S. Drapeau and J. Wiesel. Robust uncertainty sensitivity analysis. 2020.
- with I. Guo, G. Loeper and S. Wang. Joint Modelling and Calibration of SPX and VIX by Optimal Transport. 2020
- with R. Lochowski, D. Promel and P. Siorpaes. Local times and Tanaka-Meyer formulae for cadlag paths, 2019.
- with P. Siorpaes. Structure of martingale transports in finite dimensions, 2017.