Professor of Mathematics, Fellow and Tutor in Mathematics at St John's College
+44 1865 270124
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 memeber 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 is organising a major Conference on Robust Techniques in Quantitative Finance in Oxford, 3-7 September 2018. Registration is now open - please submit your paper!!!
This follows on from a series of smaller workshop, including on Martingale Optimal Transport in 2017, 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.
I also gave a couple of plenary lectures which aimed to give an overview of my contributions (and state of the art) in robust financial mathematics, including the 2011 QMF Bruti-Liberati lecture and a talk in the 2014 FM SIAM meeting.
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.
Teaching:
I lectured the "Continuous martingales and stochastic calculus" (B8.2) course in Hillary Term 2017.
Prizes, Awards, and Scholarships:
Recognition of Distinction, University of Oxford, 2015
ERC Starting Grant, 2013.
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
Major / Recent Publications:
For a complete list please see the CV
- 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 (to appear)
- with Z. Hou. On robust pricing-hedging duality in continuous time, Finance Stoch. (to appear)
- with M. Beiglboeck and T. Lim. Dual attainment for the martingale transport problem, Bernoulli (to appear)
- with S. Kallblad and T. Zariphopoulou. Dynamically consistent investment under model uncertainty: the robust forward criteria, Finance Stoch. (to appear)
- 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 A. Cox. On joint distributions of the maximum, minimum and terminal value of a continuous uniformly integrable martingale, Stoch. Process. App., 125(8): 3280-3300, 2015, DOI:10.1016/j.spa.2015.03.005
- with P. Spoida and N. Touzi. Martingale Inequalities for the Maximum via Pathwise Arguments, in: C. Donati-Martin et al (eds.), In Memoriam Marc Yor - Seminaire de Probabilite XLVIII, LNM 2137, pp. 227-247, Springer, 2015. (preprint)
- 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. PDF
- with M. Davis and V. Raval. Arbitrage Bounds for Weighted Variance Swap Prices, Mathematical Finance 24(4): 821-854; PDF
- 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)
- 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
- with A.M.G. Cox. Robust hedging of double touch barrier options, SIAM Journal on Financial Mathematics, 2: 141--182, 2011. PDF
- 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
- 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
- Fine-tune your smile: Correction to Hagan et al. Wilmott Magazine, May 2008.
- 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.
- A complete characterization of local martingales which are functions of Brownian motion and its maximum. Bernoulli, 12: 955--969, 2006. PDF
- The Skorokhod embedding problem and its offspring. Probability Surveys, 1: 321--392, 2004.
Recent pre-prints:
- with G. Guo. Computational Methods for Martingale Optimal Transport problems, 2017.
- with M. Burzoni, M. Frittelli, Z. Hou and M. Maggis. Pointwise Arbitrage Pricing Theory in Discrete Time, 2017.
- with P. Siorpaes. Structure of martingale transports in finite dimensions, 2017.
- with X. He, S. Hu and X. Zhou. Two explicit Skorokhod embeddings for simple symmetric random walk, 2017.
- with A. Aksamit and Z. Hou. Robust framework for quantifying the value of information in pricing and hedging, 2016.
- with M. Fukasawa. Efficient discretisation of stochastic differential equations, 2015.
- with X. He, S. Hu and X. Zhou. Optimal Exit Time from Casino Gambling: Strategies of Pre-Committed and Naive Gamblers. 2016