Johannes Ruf

Welcome! - Willkommen!

I am a Professor at the Department of Mathematics of the London School of Economics. 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.


Published and forthcoming papers in peer-reviewed journals

(The original publications are available on the corresponding journal websites.)

  1. 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)
  2. Simplified calculus for semimartingales: multiplicative compensators and changes of measure, Stochastic Processes and their Applications, 2023, Volume 161 (with Ales Cerny)
  3. A note on spurious model selection, Quantitative Finance, 2022, Volume 22, Issue 10 (with Weiguan Wang). Extended version
  4. Hedging with linear regressions and neural networks, Journal of Business & Economic Statistics, 2022, Volume 40, Issue 4 (with Weiguan Wang)
  5. Testing exchangeability: fork-convexity, supermartingales and e-processes, International Journal of Approximate Reasoning, 2022, Volume 141 (with Aaditya Ramdas, Martin Larsson, Wouter Koolen)
  6. Simplified stochastic calculus via semimartingale representations, Electronic Journal of Probability, 2022, Volume 27, Issue 3 (with Ales Cerny)
  7. Pure-jump semimartingales, Bernoulli, 2021, Volume 27, Issue 4 (with Ales Cerny)
  8. Relative arbitrage: sharp time horizons and motion by curvature, Mathematical Finance, 2021, Volume 31, Issue 3 (with Martin Larsson)
  9. Simplified stochastic calculus with applications in economics and finance, European Journal of Operational Research, 2021, Volume 293, Issue 2 (with Ales Cerny). Online Appendix
  10. Convergence of local supermartingales, Annales de l’Institut Henri Poincaré (B) Probabilités et Statistiques, 2020, Volume 56, Issue 4 (with Martin Larsson) (Video)
  11. Neural networks for option pricing and hedging: a literature review, Journal of Computational Finance, 2020, Volume 24, Issue 1 (with Weiguan Wang)
  12. Filtration shrinkage, the structure of deflators, and failure of market completeness, Finance and Stochastics, 2020, Volume 24, Issue 4 (with Constantinos Kardaras) (Video)
  13. The impact of proportional transaction costs on systematically generated portfolios, SIAM Journal on Financial Mathematics, 2020, Volume 11, Issue 3 (with Kangjianan Xie)
  14. 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)
  15. Nonparametric identification of the mixed hazard model using martingale-based moments, Econometric Theory, 2020, Volume 36, Issue 2 (with James Wolter). Online Appendix
  16. 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)
  17. Generalised Lyapunov functions and functionally generated trading strategies, Applied Mathematical Finance, 2019, Volume 26, Issue 4 (with Kangjianan Xie)
  18. Projections of scaled Bessel processes, Electronic Communications in Probability, 2019, Volume 24, Issue 43 (with Constantinos Kardaras). Extended version
  19. 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.
  20. Weak tail conditions for local martingales, Annals of Probability, 2019, Volume 47, Issue 3 (with Hardy Hulley)
  21. Financial models with defaultable numeraires, Mathematical Finance, 2019, Volume 29, Issue 1 (with Travis Fisher, Sergio Pulido)
  22. Local martingales in discrete time, Electronic Communications in Probability, 2018, Volume 23, Issue 31 (with Vilmos Prokaj)
  23. Volatility and arbitrage, Annals of Applied Probability, 2018, Volume 28, Issue 1 (with E. Robert Fernholz and Ioannis Karatzas)
  24. Trading strategies generated by Lyapunov functions, Finance and Stochastics, 2017, Volume 21, Issue 3 (with Ioannis Karatzas)
  25. Piecewise constant local martingales with bounded numbers of jumps, Electronic Communications in Probability, 2017, Volume 22, Issue 31
  26. 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)
  27. Distribution of the time to explosion for one-dimensional diffusions, Probability Theory and Related Fields, 2016, Volume 164, Issue 3 (with Ioannis Karatzas)
  28. A one-dimensional diffusion hits points fast, Electronic Communications in Probability, 2016, Volume 21, Issue 22 (with Cameron Bruggeman)
  29. A weak convergence criterion for constructing changes of measure, Stochastic Models, 2016, Volume 32, Issue 2 (with Jose Blanchet)
  30. Supermartingales as Radon-Nikodym densities and related measure extensions, Annals of Probability, 2015, Volume 43, Issue 6 (with Nicolas Perkowski)
  31. The uniform integrability of martingales. On a question of Alexander Cherny, Stochastic Processes and their Applications, 2015, Volume 125, Issue 10
  32. The martingale property in the context of stochastic differential equations, Electronic Communications in Probability, 2015, Volume 20, Issue 34
  33. Convergence in models with bounded expected relative hazard rates, Journal of Economic Theory, 2014, Volume 154 (with Carlos Oyarzun). Online Appendix
  34. On the hedging of options on exploding exchange rates, Finance and Stochastics, 2014, Volume 18, Issue 1 (with Peter Carr, Travis Fisher)
  35. Why are quadratic normal volatility models analytically tractable?, SIAM Journal on Financial Mathematics, 2013, Volume 4 (with Peter Carr, Travis Fisher)
  36. Negative call prices, Annals of Finance, 2013, Volume 9, Issue 4
  37. Hedging under arbitrage, Mathematical Finance, 2013, Volume 23, Issue 2
  38. 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)
  39. A new proof for the conditions of Novikov and Kazamaki, Stochastic Processes and their Applications, 2013, Volume 123. This version includes an Addendum.
  40. Conditioned martingales, Electronic Communications in Probability, 2012, Volume 17, Issue 48 (with Nicolas Perkowski)
  41. 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)
  42. Monotone imitation, Economic Theory, 2009, Volume 41, Issue 3 (with Carlos Oyarzun)

Conference proceedings and disucssions

  1. Contribution to the Discussion of ‘Safe testing’, Journal of the Royal Statistical Society: Series B (2024, with Martin Larsson and Aaditya Ramdas)
  2. 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)
  3. 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)
  4. 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)
  5. Optimal trading strategies and the Bessel process, Proceedings for the Actuarial and Financial Mathematics Conference, Brussels 2010
  6. 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)


  1. Optimal trading strategies under arbitrage, (Ph.D. dissertation 2011). Awarded Morgan Stanley Prize for Excellence in Financial Markets 2010.
  2. Structural default models with jumps (Diplom thesis 2006). Awarded DZ-Bank Karrierepreis 2007.

Technical reports

  1. Diversifying an index (2023)
  2. A remark on H1 martingales (2018, with Hardy Hulley)
  3. Convergence of local supermartingales and Novikov-Kazamaki type conditions for processes with jumps (2014, with Martin Larsson)
  4. B-splines of third order on a non-uniform grid (2008)

Papers submitted to peer-reviewed journals

  1. The numeraire e-variable and reverse information projection (2024, with Martin Larsson and Aaditya Ramdas)
  2. Mandate models and the inelastic market hypothesis (2024, with Yueying Sun)
  3. Growth in fund models (2023, with Constantinos Kardaras, Hyeng Keun Koo)
  4. Admissible anytime-valid sequential inference must rely on nonnegative martingales (2020, with Aaditya Ramdas, Martin Larsson, Wouter Koolen)
  5. Minimum curvature flow and martingale exit times (2022, with Martin Larsson)


  1. Tell me who you know and I’ll tell you who you are, JSM 2009

Future and past events

  1. 1st Seoul-London Workshop on Mathematical Finance (September 2022)
  2. Machine Learning for PDEs Workshop (September 2022)
  3. 2018 Workshop on Finance, Insurance, Probability and Statistics (FIPS 2018) (September 2018)
  4. Thera Stochastics – A Mathematics Conference in Honor of Ioannis Karatzas (May 2017)
  5. London-Paris Bachelier Workshop on Mathematical Finance (September 2016)
  6. Probability, Control and Finance. A Conference in Honor of the 60th Birthday of Ioannis Karatzas (June 2012)
  7. Minghui Yu Memorial Research Day 2009

Press coverage

  1. Forbes
  2. 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.