Alexander Cox

Professor of Probability.

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

Phone Number: 01225 386187

Office: 4 West 4.17

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

Research Areas:
My research group is broadly interested in Optimisation under Uncertainty. Our work ranges from theoretical results to applications. On the theoretical side, we have worked extensively on the Skorokhod Embedding problem, and connections to Optimal Transport. On the applied side, expertise includes Robust pricing in Mathematical Finance, and Monte Carlo methods for applications to the Neutron Transport Equation.


I am the Co-Director of the EPSRC Centre for Doctoral Training in Statistical Applied Mathematics (SAMBa), and a Co-I on the EPSRC Programme Grant, MaThRad.

Research Group:
Current Group Members:
PostDocs: Julian Hofstadler.
PhD Students: Tom Davis, Marcel Stozir, Na Eun Kim, Chaorui Wang.

Former Group Members:
PostDocs: Oliver Tough, Minmin Wang, Benjamin Dadoun.
PhD Students: Jiajie Wang (2011) [thesis], Christoph Hoeggerl (2015) [thesis], Sam Kinsley (2018) [thesis], Emma Horton (2019) [thesis], Ben Robinson (2021) [thesis], Kevin Olding (2023) [thesis], and Marco Murtinu (2023) [thesis].

Papers and Preprints:

• "Utility Maximisation with Model-independent Constraints",
  (With D. Hernandez-Hernandez). pdf. arXiv.
  
  
• "A measure-valued HJB perspective on Bayesian optimal adaptive control",
  (With S. Källblad and C. Wang). pdf. arXiv.
  
  
• "Linear and uniform in time bound for the binary branching model with Moran type interactions",
  (With E. Horton, D. Villemonais). pdf. arXiv.
  
  
• "Delayed switching identities and multi-marginal solutions to the Skorokhod embedding problem",
  (With A. M. Grass). pdf. arXiv.
  
  
• "A Bayesian Inverse Approach to Proton Therapy Dose Delivery Verification",
  (With L. Hattam, A. E. Kyprianou and T. Pryer). Proceedings of the Royal Society A, (2024) 480 (2301) .
  
  
• "Binary branching processes with Moran type interactions",
  (With E. Horton, D. Villemonais). Ann. Inst. H. Poincaré Probab. Statist., (2025) 61 (2) 917-952.
  
  
• "SDEs with no strong solution arising from a problem of stochastic control",
  (With B. A. Robinson). Electronic Journal of Probability, (2023), 28 1-24.
  
  
• "Controlled Measure-Valued Martingales: a Viscosity Solution Approach",
  (With S. Källblad, M. Larsson, S. Svaluto-Ferro). pdf. Annals of Applied Probability (2024) 34(2), 1987-2035.
  
  
• "Optimal control of martingales in a radially symmetric environment",
  (With B. A. Robinson). Stochastic Processes and their Applications, (2023), 159 149-198.
  
  
• "Using Echo State Networks to Approximate Value Functions for Control",
  (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). SIAM/ASA Journal on Uncertainty Quantification, (2022), 10(2) 775-825. pdf, code, (© 2022 Society for Industrial and Applied Mathematics). .
  
  
• "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 (2021), 81(3) 982-1001. pdf (© 2021 Society for Industrial and Applied Mathematics).
  
  
• "Multi-species neutron transport equation",
  (With S. C. Harris, E. Horton and A. E. Kyprianou). Journal of Statistical Physics (2019), 176, 425-255.
  
  
• "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), (2020) 176, 1045-1096.
  
  
• "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 (2019), 129(7) 2376-2405.
  
  
• "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, (2021) 53(1), 30-56. 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), (2019) 173, 211-259.
  
  
• "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.

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

Teaching:

• MA50251: Applied SDEs
• MA10211: Probability and Statistics 1A
• MA6000D: Stochastic Optimal Control and Applications in Finance
• MA20224: Probability 2A
• MA30087/50087: Optimisation Methods of Operational Research
• MA30089/50089: Stochastic Processes and Finance
• MA6000K: Optimal Stopping and Applications
• MA20097: Statistics 2

Other Links:

• Prob-L@b Seminars
• Prob-L@B
• RSS Applied Probability Section Meeting: Time series generation and anomaly detection in high dimensions. 16 March 2022.
• Branching structures: The sixth Bath-Beijing-Paris meeting [Neutron Transport Days] 13-17 September 2021.
• RSS Applied Probability Section Meeting: Data Analysis and Stochastic Control. 9 December 2020. Video.
• BUC8: Stochastic Optimal Control, CIMAT, Guanajuato, Mexico, 31 May - 2 June, 2017.
• Skorokhod embeddings, Martingale Optimal Transport and their applications, Oxford 14-16 March, 2016
• EPSRC Symposium Workshop - Optimal stopping, optimal control and finance, Warwick 16-20 July, 2012
• Workshop: Crossing Barriers - Hitting and stopping time problems in finance and insurance