Welcome! - Willkommen!
I am a Professor at the
Department of Mathematics of the London School of Economics and the
Deputy Director of its
Data
Science Institute. Prior to joining the mathematics department of
LSE, I was a Senior Research Fellow at the Oxford-Man Institute of
Quantitative Finance and a Senior Lecturer at the University College
London.
My research focuses on the field of stochastic analysis and its
applications to mathematical finance.
Here is an interview with me on the
Maths
at LSE Blog.
The notebooks for my PhD course on CRSP are available on
Github.
Publications
Published
and forthcoming papers in peer-reviewed journals
(The original publications are available on the corresponding journal
websites.)
- Minimum curvature flow and
martingale exit times, Electronic Journal of Probability,
2024, Volume 29, Issue 101 (with
Martin
Larsson)
- A composite generalization of
Ville’s martingale theorem using e-processes, Electronic Journal
of Probability, 2023, Volume 28, Issue 127 (with
Martin
Larsson, Wouter Koolen,
Aaditya Ramdas)
- Simplified
calculus for semimartingales: multiplicative compensators and changes of
measure, Stochastic Processes and their Applications, 2023,
Volume 161 (with Ales
Cerny)
- A note on spurious model
selection, Quantitative Finance, 2022, Volume 22, Issue 10
(with Weiguan Wang).
Extended version
- Hedging
with linear regressions and neural networks, Journal of Business
& Economic Statistics, 2022, Volume 40, Issue 4 (with
Weiguan Wang)
- Testing exchangeability: fork-convexity,
supermartingales and e-processes, International Journal of
Approximate Reasoning, 2022, Volume 141 (with
Aaditya Ramdas, Martin
Larsson, Wouter Koolen)
- Simplified
stochastic calculus via semimartingale representations,
Electronic Journal of Probability, 2022, Volume 27, Issue 3 (with
Ales Cerny)
- Pure-jump
semimartingales, Bernoulli, 2021, Volume 27, Issue 4 (with
Ales Cerny)
- Relative arbitrage: sharp
time horizons and motion by curvature, Mathematical Finance,
2021, Volume 31, Issue 3 (with
Martin
Larsson)
- Simplified
stochastic calculus with applications in economics and finance,
European Journal of Operational Research, 2021, Volume 293, Issue
2 (with Ales Cerny).
Online
Appendix
- Convergence of local
supermartingales, Annales de l’Institut Henri Poincaré (B)
Probabilités et Statistiques, 2020, Volume 56, Issue 4 (with
Martin
Larsson)
(Video)
- Neural
networks for option pricing and hedging: a literature review,
Journal of Computational Finance, 2020, Volume 24, Issue 1 (with
Weiguan Wang)
- Filtration
shrinkage, the structure of deflators, and failure of market
completeness, Finance and Stochastics, 2020, Volume 24, Issue
4 (with Constantinos
Kardaras)
(Video)
- The impact of proportional transaction costs
on systematically generated portfolios, SIAM Journal on Financial
Mathematics, 2020, Volume 11, Issue 3 (with Kangjianan Xie)
- The impact of high stakes oral
assessment on students’ approaches to learning: a case study,
Educational Studies in Mathematics, 2020, Volume 103 (with Paola
Iannone, Christoph Czichowsky)
- Nonparametric
identification of the mixed hazard model using martingale-based
moments, Econometric Theory, 2020, Volume 36, Issue 2 (with
James Wolter). Online
Appendix
- Diversification,
volatility, and surprising alpha, Journal of Investment
Consulting, 2019, Volume 19, Issue 1 (with Adrian Banner, Robert
Fernholz, Vassilios Papathanakos, David Schofield). Awarded runner-up
for the
Savvy
Investor Best Factor Investigating Paper 2018
(Video)
- Generalised Lyapunov functions and
functionally generated trading strategies, Applied Mathematical
Finance, 2019, Volume 26, Issue 4 (with Kangjianan Xie)
- Projections of scaled
Bessel processes, Electronic Communications in Probability,
2019, Volume 24, Issue 43 (with
Constantinos Kardaras).
Extended version
- Stochastic exponentials and
logarithms on stochastic intervals – a survey, Journal of
Mathematical Analysis and Applications, 2019, Volume 476, Issue 1,
Issue on Stochastic Differential Equations, Stochastic Algorithms, and
Applications (with
Martin
Larsson). This version includes an Addendum.
- Weak tail conditions for local
martingales, Annals of Probability, 2019, Volume 47, Issue 3
(with Hardy
Hulley)
- Financial models with
defaultable numeraires, Mathematical Finance, 2019, Volume
29, Issue 1 (with Travis Fisher,
Sergio
Pulido)
- Local martingales in discrete time,
Electronic Communications in Probability, 2018, Volume 23, Issue
31 (with Vilmos
Prokaj)
- Volatility and
arbitrage, Annals of Applied Probability, 2018, Volume 28,
Issue 1 (with E. Robert Fernholz and
Ioannis Karatzas)
- Trading strategies generated by
Lyapunov functions, Finance and Stochastics, 2017, Volume
21, Issue 3 (with Ioannis
Karatzas)
- Piecewise constant local
martingales with bounded numbers of jumps, Electronic
Communications in Probability, 2017, Volume 22, Issue 31
- Pathwise solvability of
stochastic integral equations with generalized drift and non-smooth
dispersion functions, Annales de l’Institut Henri Poincaré (B)
Probabilités et Statistiques, 2016, Volume 52, Issue 2 (with
Ioannis Karatzas)
- Distribution
of the time to explosion for one-dimensional diffusions,
Probability Theory and Related Fields, 2016, Volume 164, Issue 3
(with Ioannis
Karatzas)
- A one-dimensional
diffusion hits points fast, Electronic Communications in
Probability, 2016, Volume 21, Issue 22 (with Cameron Bruggeman)
- A weak convergence criterion for
constructing changes of measure, Stochastic Models, 2016,
Volume 32, Issue 2 (with Jose
Blanchet)
- Supermartingales as Radon-Nikodym
densities and related measure extensions, Annals of
Probability, 2015, Volume 43, Issue 6 (with
Nicolas
Perkowski)
- The uniform integrability of
martingales. On a question of Alexander Cherny, Stochastic
Processes and their Applications, 2015, Volume 125, Issue 10
- The martingale property in
the context of stochastic differential equations, Electronic
Communications in Probability, 2015, Volume 20, Issue 34
- Convergence in models with bounded expected
relative hazard rates, Journal of Economic Theory, 2014,
Volume 154 (with
Carlos
Oyarzun). Online Appendix
- On the hedging of options on exploding
exchange rates, Finance and Stochastics, 2014, Volume 18,
Issue 1 (with Peter
Carr, Travis Fisher)
- Why are quadratic normal volatility models
analytically tractable?, SIAM Journal on Financial
Mathematics, 2013, Volume 4 (with
Peter Carr, Travis
Fisher)
- Negative call prices,
Annals of Finance, 2013, Volume 9, Issue 4
- Hedging under arbitrage,
Mathematical Finance, 2013, Volume 23, Issue 2
- A practical guide to measuring
social structure using indirectly observed network data, Journal
of Statistical Theory and Practice, 2013, Volume 7, Issue 1 (with
Tyler McCormick, Amal
Moussa,
Thomas
DiPrete, Andrew
Gelman,
Julien
Teitler, Tian
Zheng)
- A new proof for the conditions of
Novikov and Kazamaki, Stochastic Processes and their
Applications, 2013, Volume 123. This version includes an
Addendum.
- Conditioned martingales,
Electronic Communications in Probability, 2012, Volume 17, Issue
48 (with Nicolas
Perkowski)
- Pricing corporate bonds in an
arbitrary jump-diffusion model based on an improved Brownian-bridge
algorithm, Journal of Computational Finance, 2011, Volume 14,
Issue 3 (with Matthias
Scherer)
- Monotone imitation,
Economic Theory, 2009, Volume 41, Issue 3 (with
Carlos
Oyarzun)
Conference proceedings
and disucssions
- Contribution to the
Discussion of ‘Safe testing’, Journal of the Royal Statistical
Society: Series B (2024, with
Martin
Larsson and Aaditya
Ramdas)
- Contribution to the
Discussion of ‘Estimating means of bounded random variables by
betting’, Journal of the Royal Statistical Society: Series B
(2023, with
Martin
Larsson)
- On
augmenting the references section with a citation network
visualization, Ninth International Conference on Learning
Representations (ICLR 2021). Workshop: Rethinking ML Papers (with
Putra Manggala, Tigran Atoyan, Gracia Samosir, Jan Varsava)
- A systematic way to construct
markets with arbitrage, Arbitrage, Credit and Informational
Risks. Proceedings of the Sino-French Research Program in Financial
Mathematics Conference, Beijing June 2013 (with
Wolfgang
Runggaldier)
- Optimal trading
strategies and the Bessel process, Proceedings for the Actuarial
and Financial Mathematics Conference, Brussels 2010
- Comparing two methods for
predicting opinions using social structure, JSM Proceedings
2009 (with Tyler
McCormick, Amal Moussa,
Thomas
DiPrete, Andrew
Gelman,
Julien
Teitler, Tian
Zheng)
Theses
Technical reports
Papers submitted to
peer-reviewed journals
Poster
- Tell me who you know and I’ll tell you
who you are, JSM 2009
Future and past events
Press coverage
- Forbes
- Risk
magazine
Industrial experience
Consulting for a hedgefund. Moreover, during several internships I
had great opportunites not only facing exciting challenges but also
participating in the transformation of theoretical knowledge into
valuable products.
- Morgan Stanley, Investment banking
division, Securitized Products Group, Strategy (2009, 2010)
- J.P. Morgan, Investment
banking division, Quantitative Research, Equities (2008)
- d-fine GmbH, Consulting in
quantitative and technical risk management (2006)
- Commerzbank, Investment
banking division, Quantitative Research, FX (2004)
- Rohde & Schwarz
(1998, 1999)÷