Research Group:
Current Group Members:
PostDocs: Oliver Tough.
PhD Students: Tom Davis, Marcel
Stozir, Na Eun Kim, Chaorui Wang.
Former Group Members:
PostDocs: 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:
 "Delayed switching identities and multimarginal 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). pdf. arXiv.
 "Binary branching processes with Moran type
interactions",
(With E. Horton, D. Villemonais). pdf, arXiv.
 "SDEs with no strong solution arising from a problem
of stochastic control",
(With B. A. Robinson). pdf, arXiv.
 "Controlled MeasureValued Martingales: a
Viscosity Solution Approach",
(With
S. Källblad, M. Larsson, S. SvalutoFerro). pdf, arXiv. (To Appear, Annals of Applied Probability).
 "Optimal control of martingales in a radially
symmetric environment",
(With B. A. Robinson). Stochastic
Processes and their Applications, (2023), 159 149198.
 "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.
 "MonteCarlo 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) 775825. 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 manytoone and keff",
(With E. Horton, A. E. Kyprianou and D. Villemonais). SIAM
Journal on Applied Mathematics (2021), 81(3) 9821001. pdf (© 2021
Society for Industrial and Applied Mathematics).
 "Multispecies neutron transport equation",
(With S. C. Harris, E. Horton and A. E. Kyprianou). Journal of Statistical
Physics (2019), 176, 425255.
 "Measurevalued martingales and optimality of Basstype solutions to the Skorokhod Embedding Problem",
(With M. Beiglböck, M. Huesmann and S. Källblad).
pdf, arXiv.
 "The geometry of multimarginal Skorokhod Embedding",
(With M. Beiglböck and M. Huesmann). Probability Theory and
Related Fields (Open Access), (2020) 176, 10451096.
 "Robust Hedging of Options on a Leveraged Exchange
Traded Fund",
(With S. M. Kinsley). pdf. Annals of
Applied Probability (2019) 29(1),
531576.
 "Discretisation and Duality of Optimal Skorokhod Embedding Problems",
(With S. M. Kinsley).
Stochastic
Processes and their Applications (2019), 129(7) 23762405.
 "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).
 "Modelindependent pricing with insider information: a Skorokhod embedding approach",
(With B. Acciaio and M. Huesmann). Advances in
Applied Probability, (2021) 53(1), 3056. code.
 "Modelindependent bounds for Asian options: a dynamic programming approach",
(With S. Källblad). SIAM Journal on Control
and Optimisation, (2017) 55 (6), 34093436.
pdf. (©
2017 Society for Industrial and Applied Mathematics).
 "The Root solution to the multimarginal embedding problem: an optimal stopping and timereversal approach",
(With J. Obłój and
N. Touzi). Probability Theory and Related Fields (Open
Access), (2019) 173, 211259.
 "Pathwise superreplication 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) 208:327400.
 "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, 113. arXiv.
 "Modelindependent noarbitrage conditions on American put options",
(With C. Hoeggerl).
Mathematical Finance, (2016) 26 (2), 431458.
 "Embedding Laws in Diffusions by Functions of Time",
(With G. Peskir). Annals of
Probability, (2015) 43 (5), 24812510. pdf .
 "Root's Barrier: Construction, Optimality and Applications
to Variance Options",
(With J. Wang), Annals of
Applied Probability
(2013) 23 (3), 859894.
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).
 "TimeHomogeneous Diffusions with a Given Marginal at a
Random Time",
(With D. Hobson
and
J. Obłój),
ESAIM: Probability and Stochastics
, (2011) 15:
S11S24. The original publication is available
at
www.edpsciences.org/ps
. pdf
.
 "Robust pricing and hedging of double notouch
options",
(With J. Obłój). Finance
and Stochastics (2011) 15 3 573605. pdf , arXiv .
 "Robust hedging of double touch barrier options".
(With
J. Obłój).
SIAM Journal of Financial Mathematics
(2011) 2,
141182.
 "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), 18701896.
 "Classes of measures which can be embedded in the
Simple Symmetric Random Walk",
(With J.Obłój)
Electronic
Journal of Probability (2008) 12031228.
 "A unifying class of Skorokhod embeddings: connecting the
AzemaYor and Vallois
embeddings",
(With D.Hobson).
Bernoulli
13 1 (2007) 114130
.
pdf
.
 "Extending ChaconWalsh: 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) 477492.
 "Skorokhod Embeddings, Minimality and Noncentred Target
Distributions",
(with
D.Hobson).
Probability
Theory and Related Fields 135 3 (2006) 395414.
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 email me for more
information. 

Teaching:
Other Links:

ProbL@b Seminars

ProbL@B

RSS Applied Probability Section Meeting: Time series generation and anomaly detection in high dimensions. 16 March 2022.

Branching
structures: The sixth BathBeijingParis meeting [Neutron
Transport Days] 1317 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 1416 March, 2016

EPSRC Symposium Workshop  Optimal stopping, optimal control and
finance, Warwick 1620 July, 2012

Workshop: Crossing Barriers  Hitting and stopping time problems
in finance and insurance
