Curriculum Vitae
Curriculum Vitae
University of Cambridge, Trinity College (1999–2002): Ph.D. in low-dimensional topology
Thesis: Triangulations of 3-manifolds
University of Cambridge, Magdalene College (1998–1999): Cambridge Certificate of Advanced Study in Mathematics: Part III of the Mathematical Tripos
Grade: Distinction
University of Ljubljana, Slovenia (1993–1997): Diploma in Pure Mathematics
Grade: summa cum laude
Professor of Probability, University of Warwick (Aug 2018– present)
Department of Statistics
Chair in Probability, King’s College London (Jan 2016–Jul 2018)
Financial Mathematics Group, Department of Mathematics
Reader in Probability, Imperial College London (Apr 2012–Dec 2015)
Pure Mathematics Section, Department of Mathematics
Associate Professor, University of Warwick (Jul 2010–Mar 2012)
Department of Statistics
Lecturer, Imperial College London (Aug 2007–Jun 2010)
Mathematical Finance Section, Department of Mathematics
Research Fellow, Imperial College London (Oct 2005–Jul 2007)
Institute for Mathematical Sciences: applications of functional analysis and spectral theory to problems in mathematical finance and stochastic approximation
Quantitative Research Analyst, Royal Bank of Scotland (Aug 2004–Sep 2005)
Foreign Exchange Options Desk, London: front-office role; developed models for the pricing and hedging of FX derivatives
Burroughs Wellcome Postdoctoral Fellow, Florida State University (Aug 2003–Apr 2004)
Department of Mathematics, Program in Mathematics and Molecular Biology (PMMB): applications of low-dimensional topology to problems in molecular biology
Researcher, Trinity College Cambridge (Oct 2002–Sep 2003)
One-year funding for research in low-dimensional topology
Mathematical Finance II (continuous time): Course Lecturer, B.Sc. in Mathematics, years 3 & 4 and MSc in Mathematics, King’s College London (spring term 2018)
The course is a rigorous introduction to continuous-time mathematical finance, along with the associ- ated probabilistic background, c. 120 students in attendance
Mathematical Finance I (discrete time): Course Lecturer, B.Sc. in Mathematics, years 3 & 4 and MSc in Mathematics, King’s College London (autumn term 2017)
Topics covered: conditional expectation, elements of discrete-time martingale theory, the binomial asset pricing model, option pricing in discrete time, discrete-time term structure models and discrete-time portfolio theory. The course was attended by 150 students
Measure & Integration: Course Lecturer, B.Sc. in Mathematics, years 3 & 4 and MSc in Pure Mathematics, Imperial College London (autumn term 2015)
The course proves the Carathéodory extension theorem and constructs the Lebesgue measure on Rd, defines Lebesgue integrals and proves the convergence and Fubini theorems. It discusses modes of convergence, the Lebesgue decomposition and Radon-Nikodym theorems. The course was attended by c. 40 students, mostly interested in pure mathematics
Probability: Course Lecturer, B.Sc. in Mathematics, years 3 & 4 and MSc in Pure Mathematics and MSc in Statistics, Imperial College London (spring term 2015)
The course covers measure theoretic probability with an emphasis on martingale theory in discrete time, e.g Doob’s optional sampling theorem and the martingale convergence theorem are proved
Stochastic Differential Equations: Module Lecturer, Mathematics Taught Course Centre (spring terms 2013 and 2015)
A Ph.D.-level course delivered simultaneously (via video link) to the Universities of Oxford, Warwick, Imperial and Bath. Topics include: strong and weak solutions of stochastic differential equations, martingale theory in continuous time, local time and the occupation times formula, time-change tech- niques, stochastic exponentials
Pricing and Hedging in Financial Markets: Module Lecturer, M.Sc. in Statistics, Department of Mathematics, Imperial College London (spring term 2013)
Elective module covering the fundamentals of risk-neutral pricing theory for contingent claims in complete and incomplete markets in the context of trinomial tree random walk models
Statistical Frontiers: Stochastic Volatility Models with Jumps: Module Lecturer, Ph.D. pro- gramme in Mathematics and Statistics (MASDOC), University of Warwick (spring term 2011)
Topics include: Lévy processes, stochastic volatility models, option pricing algorithms
Probability Theory: Course Lecturer, B.Sc. in Mathematics and Statistics/MORSE, years 3 & 4, University of Warwick (spring term 2011)
The course covers the measure theoretic fundamentals of probability: independence and conditioning, probability measures on metric spaces, types of probabilistic convergence, an introduction to martin- gale theory in discrete time. Core module for the Actuarial stream, attended by c. 60 to 70 students
Statistical Models in Finance: Course Lecturer, M.Sc. in Mathematics and Finance, Imperial College London (spring term 2010)
The course develops statistical tools used in the financial markets with emphasis on risk management applications. Topics include: linear regression, likelihood and Bayesian inference, financial time series modelling (ARMA models, GARCH models and volatility forecasting), maximum likelihood and other methods for parameter estimation in continuous-time models
One-Dimensional Diffusion Processes and Stochastic Logarithms: Course Lecturer, London Graduate School in Mathematical Finance (spring term 2010)
A Ph.D. course that develops aspects of martingale theory in continuous time and proves recent results on the characterisation of the martingale property of stochastic exponentials
Stochastic Processes: Course Lecturer, M.Sc. in Mathematics and Finance, Imperial College London (autumn terms 2008, 2009)
Core module in the M.Sc. programme covering the theory of processes in continuous time. Topics include: martingale theory in continuous time (Doob’s optional sampling theorem and martingale inequalities), construction of Brownian motion and its path properties, Markov processes, construction and properties of stochastic integrals, fundamentals of the theory of Stochastic Differential Equations. The main probability course taught in the M.Sc. programme
Spectral Methods for Mathematical Finance: Course Lecturer, M.Sc. in Mathematics and Finance, Imperial College London (spring terms 2007, 2008)
Course on the implied volatility surface generated by the models most widely used in the financial markets for the pricing of derivatives
“Exact simulation of the maximum of a stable process: convex minorants and coupling from the past” Workshop on Bayesian Computation for High-Dimensional Statistical Models, National University of Singapore, Aug 2018
“Asymptotic variance for random walk Metropolis chains in high dimensions: logarithmic growth via the Poisson equation” Third Conference on Ambit Fields and Related Topics, Aarhus, Denmark, Aug 2018
“Coupling and the Policy Improvement Algorithm in continuous time” Bachelier Seminar, Institut Henri Poincaré, Paris, March 2018
“Invariance principle for non-homogeneous random walks” Near-Critical Stochastic Systems: A Workshop in Celebration of M. Menshikov’s 70th birthday, Royal Holloway University of London, Mar 2018
“Invariance principle for non-homogeneous random walks” Stochastic Analysis Seminar, Mathematical Institute, Oxford, Nov 2017
“Stability of the overshoots of recurrent random walks” Probability Seminar at UNAM, Mexico City, Nov 2017
“Stability of the overshoots of recurrent random walks” Durham Symposium on Markov Processes, Mixing Times and Cutoff, Jul 2017
“Invariance principle for non-homogeneous random walks” Probability in the North East workshop, Durham, Sep 2016
“Invariance principle for non-homogeneous random walks” The 8th International Conference on Lévy Processes, Angers, France, Jul 2016
“Markov-Chain Monte Carlo optimisation methods for energy markets” Workshop on Energy Management: Flexibility, Risk and Optimisation, International Centre for Mathematical Sciences, Edinburgh, Jun 2016
“Weak multilevel Monte Carlo schemes for Lévy-driven SDEs” Workshop on Stochastic Analysis and Applications, Beijing Normal University, Beijing, China, Mar 2016
“Weak multilevel Monte Carlo schemes for Lévy-driven SDEs” Workshop on Mathematical Finance and Related Issues, Osakg University, Japan, Mar 2015
“Buffer-overflows: joint limit law of the overshoot and undershoot of reflected Lévy processes” Greek Stochastics ζ, Athens, Greece, Dec 2014
“Weak multilevel Monte Carlo schemes for Lévy-driven SDEs” Stochastic Calculus, Martingales, and Financial Modeling Conference, St Petersburg, Russia, Jul 2014
“Markov chain approximations to scale functions of Lévy processes” Model Approximation and Numerical Methods Workshop, part of the Advanced Modeling and Numerical Methods programme, Paris, Mar 2014
“Asymptotic independence of three statistics of the maximal increments of random walks and Lévy processes” Stochastic Analysis Seminar, Mathematical Institute, Oxford, Oct 2013
“A new look at short-term implied volatility in asset price models with jumps” PDE and Mathematical Finance V Conference, Stockholm, Jun 2013
“Loss of the semi-martingale property at the hitting time of a level” Statistics Seminar, Durham University, Apr 2013
“Loss of the semi-martingale property at the hitting time of a level” Probability Seminar, University of Essen, Germany, Dec 2012
“Coupling and tracking of regime-switching martingales” The Developments in Coupling Workshop, York, Sep 2012
“Mirror and synchronous coupling of geometric Brownian motion” Workshop on Stochastic and PDE Methods in Financial Mathematics, Yerevan, Armenia, Sep 2012
“Coupling and tracking of regime-switching martingales” Optimal Stopping, Optimal Control and Finance Conference, Warwick, Jul 2012
“Short-term implied volatility in asset price models with jumps” SIAM Conference on Financial Mathematics and Engineering, Minneapolis, USA, Jul 2012
“Asymptotic properties of the implied volatility surface in stochastic volatility models with jumps” Risk and Stochastics Conference, London School of Economics, Mar 2012
“Pricing and hedging of barrier options in foreign exchange” Presentation to quantitative research team, Mako Investment Managers, London, Dec 2011
“Sextuple law of a certain path-functional of a totally asymmetric Lévy process” Probability Seminar, University of Vienna, Oct 2011
“American options in stochastic volatility models with jumps” Special session on Lévy processes in Stochastic Finance, Conference on Markov & semi-Markov Processes & Related Fields, Chalkidiki, Greece, Sep 2011
“Maximal increments of random walks and Lévy processes” The 14th Brazilian Time Series and Econometrics School, Gramado, Brazil, Aug 2011
“Large deviations and the asymptotics of implied volatility under affine stochastic volatility models” Session on stochastic volatility in the 35th Conference on Stochastic Processes and their Applications, Oaxaca, Mexico, Jun 2011
“Limiting distributions of continuous-state branching processes with immigration” Kolloquium, Institut für Finanzmathematik, Universität Ulm, May 2011
“On the first passage of completely asymmetric reflected Lévy processes” Workshop on Optimal Stopping, Sequential Methods and Related Topics, University of Freiburg, Apr 2011
“On the first passage of completely asymmetric reflected Lévy processes” Bachelier Seminar, Institut Henri Poincaré, Paris, Apr 2011
“Limiting distributions of continuous-state branching processes with immigration” Laboratoire de Probabilités et Modèles Aléatoires, Paris VII, Apr 2011
“On the first passage of completely asymmetric reflected Lévy processes” Probability Forum, Department of Statistics, University of Warwick, Jan 2011
“Limiting distributions of continuous-state branching processes with immigration” Seminar for Stochastic Analysis and Mathematical Finance, Institute of Mathematics, Humboldt Uni- versity, Berlin, Dec 2010
“Asymptotics of the implied volatility smile under affine stochastic volatility models with jumps” Midlands Probability Theory Seminar, Department of Mathematics, University of Warwick, Oct 2010
“Deterministic criteria for the absence of arbitrage in diffusion models” Sixth World Congress of the Bachelier Finance Society, Toronto, June 2010
“Volatility derivatives in market models with jumps” Fields Institute Thematic Program on Quantitative Finance: Foundations and Applications, Workshop on Financial Derivatives and Risk Management, Toronto, May 2010
“Deterministic criteria for the absence of arbitrage in diffusion models” Fifth Annual AMaMeF Conference, Bled, Slovenia, May 2010
“Deterministic criteria for the existence of arbitrage in diffusion models” Maths 2010, British Mathematics Colloquium & British Applied Mathematics Colloquium, Maxwell Institute for Mathematical Sciences, Edinburgh, Apr 2010
“Continuously monitored barrier options under Markov processes” Seminar, Department of Statistics, Columbia University, New York, Mar 2010
“Convergence rates for two-sided first-passage densities” Workshop on Crossing barriers: Hitting and Stopping Time Problems in Finance and Insurance, University of Bath, Jan 2010
“Simulation of Lévy processes” Graduate course, Department of Mathematics, Fudan University, Shanghai, China, Apr 2019 (8 lectures)
“Multi-level Monte Carlo for processes with jumps” Ph.D.-level course, Mathematical Insitute, UNAM, Mexico City, Jan 2017 (6 lectures)
“Stochastic Differential Equations” Graduate course, Barcelona Graduate School of Mathematics, University of Barcelona, Jan 2014 (6 lectures)
“Weak approximation of Lévy processes” Advanced course at the workshop Greek Stochastics ε: Statistical Inference for Jump Processes, Kalamata, Greece, Jul 2013 (4 lectures) “Trinomial trees, Brownian motion and the Black-Scholes formula” The 14th Brazilian Time
Series and Econometrics School, Gramado, Brazil, Aug 2011 (4 lectures)
“Fluctuation theory in stochastic volatility models with jumps” Summer School in Stochastic Finance, The Institute of Mathematical Finance, Ulm University, Sep 2010 (3 lectures)
“Brownian motion and stochastic integration” Summer School in Financial Mathematics, Faculty of Mathematics and Physics University of Ljubljana, Sep 2009 (10 lectures)
Member of the Scientific Steering Committee of the Isaac Newton Institute, Cambridge
Appointed January 2019, duration of appointment 3 years
Assessing proposals for future programmes submitted to the Institute and shaping its scientific agenda
Full College member of the EPSRC College
Serving on EPSRC panels for the evaluation of scientific proposals in mathematics; involved in setting the EPSRC agenda in Applied Probability and Statistics
Mathematics sub-panel for REF 2021
Nominated by the London Mathematical Society to serve on the Mathematics sub-panel for REF 2021
Assessing the research output submissions of UK universities in mathematical sciences as part of the national assessment exercise of universities that determines their government funding
Founded London Probability at King’s (LP@K)
Funding body: KCL Faculty of Natural and Mathematical Sciences and EPSRC
Project: LP@K is a research centre on probability theory and its applications in the sciences and engineering. Strong interdisciplinary focus, with emphasis on impact beyond mathematics
Founding Director of the Imperial Probability Centre
Funding body: Faculties of Natural Sciences and Engineering, Imperial College London
Founding member of the Applied Probability Section of the Royal Statistical Society
One of 8 founding members of the section, involved in setting up the section and organising its activities, e.g. “Quantitative challenges in post-crisis financial markets” event at the RSS on 17 Oct 2014, consisting of a series of talks by distinguished academics and practitioners (2011–2014)
Associate Editor IMA Journal of Applied Mathematics (2011–2020), International Journal of Theoretical and Applied Finance (2009–present)
External Examiner
London School of Economics MSc in Financial Mathematics at the Department of Mathemat- ics (2012–2016)
Member of Ph.D. defence committee
Examined more than 20 Ph.D. theses both nationally and internationally in the areas of probability and its applications and financial mathematics
Co-organiser, Mean-Field Games, Energy and Environment, The Alan Turing Institute (Feb 2018)
A large workshop (100 participants) at The Turing on mean-field games and applications (3-day event), sponsored by the Programmes on Data-Centric Engineering and Defence & Security at The Turing. Keynote speaker is P.-L. Lions.
Co-organiser, Limit Theorems in Probability, Department of Mathematics, Imperial College London (Mar 2015)
Large international 4-day conference (more than 100 participants) on the central topic in probability theory, commemorating the 70th birthday of Professor N. H. Bingham, sponsored by EPSRC and LMS.
Co-organiser, UK Probability Meeting 2014, Department of Mathematics, Imperial College London (Sep 2014)
A major international conference in probability (5-day event), sponsored by EPSRC and LMS.
Co-organiser, Computational Methods for Jump Processes, Department of Statistics, Univer- sity of Warwick (Jul 2014)
A 2-day workshop on simulation and estimation of processes with jumps. Funded by CRISM.
Organiser, London Probability Seminar, Department of Mathematics, Imperial College Lon- don (Oct 2013–Dec 2015).
A series of one-day workshops featuring graduate-level lectures by an international expert, followed by a set of research talks on a given theme. Two workshops per term. Themes covered: Coupling, Branching, Random Graphs, Random Dynamical Systems, Markov Chain Monte Carlo.
Organiser, Workshop on Stochastic Methods in Financial Markets, Department of Mathematics, University of Ljubljana, Slovenia (Aug 2011)
International workshop sponsored by the Department of Mathematics, University of Ljubljana, the Department of Statistics, University of Warwick and EPSRC.
Co-organiser, Summer School on Stochastic Methods in Financial Markets, Department of Mathematics, University of Ljubljana, Slovenia (Aug–Sep 2011):
Member of the organising committee, The Fifth General AMaMeF Conference 2010, Bled, Slovenia (May 2010).
One of the largest international conferences in mathematical finance in 2010 with over 400 participants and 130 presentations, sponsored by the European Science Foundation
Organiser, Stochastic Finance Seminar, Department of Statistics, University of Warwick (2011– 2012), & Finance and Stochastics Seminar, Department of Mathematics, Imperial College London (2007–2010)