Alexander Cox

Reader in Probability

Address:
Department of Mathematical Sciences,
University of Bath,
Claverton Down,
Bath BA2 7AY.

Phone Number: 01225 386187

Office: 6 West 1.13

E-Mail:
A.M.G.Cox@bath.ac.uk

Research Areas:
Probability Theory and applications to Mathematical Finance.

Papers and Preprints:

"Echo State Networks for Reinforcement Learning",
(With A. G. Hart, K. R. Olding, O. Isupova and J. H. P. Dawes). pdf, arXiv.
"Monte-Carlo Methods for the Neutron Transport Equation",
(With A. E. Kyprianou, S. C. Harris and M. Wang). pdf, arXiv, code.
"Switching Identities by Probabilistic Means",
(With J. Backhoff, A. Grass and M. Huesmann). pdf, arXiv.
"Stochastic Methods for Neutron Transport Equation III: Generational many-to-one and k-eff",
(With E. Horton, A. E. Kyprianou and D. Villemonais). SIAM Journal on Applied Mathematics (To Appear). pdf, arXiv.
"Multi-species neutron transport equation",
(With S. C. Harris, E. Horton and A. E. Kyprianou). Journal of Statistical Physics (To Appear).
"Measure-valued martingales and optimality of Bass-type solutions to the Skorokhod Embedding Problem",
(With M. Beiglböck, M. Huesmann and S. Källblad). pdf, arXiv.
"The geometry of multi-marginal Skorokhod Embedding",
(With M. Beiglböck and M. Huesmann). Probability Theory and Related Fields (Open Access), (2019).
"Robust Hedging of Options on a Leveraged Exchange Traded Fund",
(With S. M. Kinsley). pdf. Annals of Applied Probability (2019), 29(1), 531-576.
"Discretisation and Duality of Optimal Skorokhod Embedding Problems",
(With S. M. Kinsley). Stochastic Processes and their Applications (To Appear), (2018).
"Martingale optimal transport with stopping",
(With E. Bayraktar and Y. Stoev). SIAM Journal on Control and Optimisation, 56(1), 417–433. pdf. (© 2018 Society for Industrial and Applied Mathematics).
"Model-independent pricing with insider information: a Skorokhod embedding approach",
(With B. Acciaio and M. Huesmann). Advances in Applied Probability (To Appear). pdf, arXiv, code.
"Model-independent bounds for Asian options: a dynamic programming approach",
(With S. Källblad). SIAM Journal on Control and Optimisation, (2017) 55 (6), 3409-3436. pdf. (© 2017 Society for Industrial and Applied Mathematics).
"The Root solution to the multi-marginal embedding problem: an optimal stopping and time-reversal approach",
(With J. Obłój and N. Touzi). Probability Theory and Related Fields (Open Access), (2018).
"Pathwise super-replication via Vovk's outer measure",
(With M. Beiglböck, M. Huesmann, N. Perkowski and D. Prömel). Finance and Stochastics (Open Access), (2017).
"Optimal Transport and Skorokhod Embedding",
(With M. Beiglböck and M. Huesmann). Inventiones Mathematicae (Open Access), (2017) 208:327-400.
"On joint distributions of the maximum, minimum and terminal value of a continuous uniformly integrable martingale",
(With J. Obłój). Stochastic Processes and their Applications (2015).
"Robust pricing and hedging under trading restrictions and the emergence of local martingale models",
(With J. Obłój and Z. Hou). Finance and Stochastics, (2016). pdf.
"Optimal robust bounds for variance options",
(With J. Wang). pdf, arXiv, code.
"From minimal embeddings to minimal diffusions",
(With M. Klimmek). Electronic Communications in Probability, (2014) 19, 1-13. arXiv.
"Model-independent no-arbitrage conditions on American put options",
(With C. Hoeggerl). Mathematical Finance, (2016) 26 (2), 431-458.
"Embedding Laws in Diffusions by Functions of Time",
(With G. Peskir). Annals of Probability, (2015) 43 (5), 2481-2510. pdf .
"Root's Barrier: Construction, Optimality and Applications to Variance Options",
(With J. Wang), Annals of Applied Probability (2013) 23 (3), 859-894. pdf .
"Utility theory front to back — inferring utility from agents' choices",
(With D. Hobson and J. Obłój). International Journal of Theoretical and Applied Finance (IJTAF), (2014) 17 (3).
"Time-Homogeneous Diffusions with a Given Marginal at a Random Time",
(With D. Hobson and J. Obłój), ESAIM: Probability and Stochastics , (2011) 15: S11-S24. The original publication is available at www.edpsciences.org/ps . pdf .
"Robust pricing and hedging of double no-touch options",
(With J. Obłój). Finance and Stochastics (2011) 15 3 573-605. pdf , arXiv .
"Robust hedging of double touch barrier options".
(With J. Obłój). SIAM Journal of Financial Mathematics (2011) 2, 141-182.
"Arbitrage bounds".
In Encyclopedia of Quantitative Finance (2010), John Wiley & Sons, Ed. R. Cont
"Pathwise inequalities for local time: applications to Skorokhod embeddings and optimal stopping",
pdf . (With D. Hobson and J. Obłój). Annals of Applied Probability (2008) 18 (5), 1870-1896.
"Classes of measures which can be embedded in the Simple Symmetric Random Walk",
(With J.Obłój) Electronic Journal of Probability (2008) 1203-1228.
"A unifying class of Skorokhod embeddings: connecting the Azema-Yor and Vallois embeddings",
(With D.Hobson). Bernoulli 13 1 (2007) 114-130 . pdf .
"Extending Chacon-Walsh: minimality and generalised starting distributions",
Séminaire de Probabilités XLI , Springer, 2008. arXiv .
"Local Martingales, Bubbles and Option Prices",
(With D.Hobson) Finance and Stochastics 9 4 (2005) 477-492.
"Skorokhod Embeddings, Minimality and Non-centred Target Distributions",
(with D.Hobson). Probability Theory and Related Fields 135 3 (2006) 395-414. arXiv .
"An Optimal Skorokhod Embedding for Diffusions",
(With D.Hobson). Stochastic Processes and their Applications 111 (2004) 17 - 39.

Copies available on request

You might also be interested in my PhD thesis, most of which has also appeared in some of the papers above, or the theses of my former students Jiajie Wang (2011), Christoph Hoeggerl (2015), and Sam Kinsley (2018).

I am always interested in taking on PhD students in Probability or Mathematical Finance. You can find some possible projects here; alternatively, please e-mail me for more information.

Teaching:

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