Alexander Cox

Senior Lecturer 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:

• "Model-independent pricing with insider information: a Skorokhod embedding approach",
  (With B. Acciaio and M. Huesmann). pdf, arXiv.
  
  
• "Model-independent bounds for Asian options: a dynamic programming approach",
  (With S. Källblad). pdf, arXiv.
  
  
• "The Root solution to the multi-marginal embedding problem: an optimal stopping and time-reversal approach",
  (With J. Obłój and N. Touzi). pdf, arXiv.
  
  
• "Pathwise super-replication via Vovk's outer measure",
  (With M. Beiglböck, M. Huesmann, N. Perkowski and D. Prömel). pdf, arXiv.
  
  
• "Optimal Transport and Skorokhod Embedding",
  (With M. Beiglböck and M. Huesmann). To Appear, Inventiones Mathematicae. pdf, arXiv.
  
  
• "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) and Christoph Hoeggerl (2015).

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:

• 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
• 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