Members

Members

To find out more about the research interests of group members shown below, please visit their personal website from the links below.

 
Brigo
 

Prof Damiano Brigo

Damiano's research in stochastic analysis started with the differential geometric approach to statistics and its use in stochastic dynamical systems, and stochastic filtering in particular, where he co-originated the Projection Filter approach to filtering in the nineties. Research is still active on approximate finite dimensional filters that are obtained by projecting the infinite dimensional stochastic PDE of the filtering problem onto a finite dimensional manifold of probability densities according to a variety of metrics and manifolds. Analytical and numerical studies of the obtained approximations are considered.

Damiano's main interests are in mathematical finance and in particular concern derivatives valuation and hedging, funding costs and BSDEs, counterparty risk pricing and collateral modelling, and the new holistic and non-linear modelling approach emerging from the above points. Further interests include stochastic models for commodities and inflation, dependence dynamics, characterization of self-chaining arrival times, optimal execution and algorithmic trading, liquidity risk measurement and risk measurement in general.

Visit Prof Brigo's webpage
E-mail
Phone: (+44) (0)20 7594 2932

Cass
 

Dr Thomas Cass

Thomas' research comprises both classical areas of Stochastic Analysis such as Malliavin Calculus and newly-emerging disciplines such as Rough Path Theory. He is also interested in the ways in which these mathematical insights can spur developments in numerical simulation in Mathematical Finance. More specifically, some of his interests include:

• The theory of Rough Differential Equations (RDEs), both deterministic and stochastic; the general properties of RDEs driven by Gaussian noise and generalisations of Hoermander's Theorem to the existence and smoothness of the laws of such  processes.

• The use of Malliavin Calculus and cubature methodologies for developing  efficient Monte Carlo based pricing methods in Mathematical Finance.

• Rough Path Theory to understand models of interacting agents with individual preferences. Rough Paths in a geometric setting; Rough Paths on manifolds.

Visit Dr Cass' webpage
E-mail
Phone: (+44) (0)20 7594 7849

Cont
 

Prof Rama Cont

Rama's research focuses on stochastic analysis, stochastic processes and mathematical modeling in finance, in particular the modeling of extreme market risks: discontinuities in market behavior, extreme risks, endogenous risk and systemic risk.

Visit Prof Cont's webpage
E-mail
Phone: (+44) (0)207 594 0802

Crisan

Prof Dan Crisan

Dan’s research lies in the area of the theoretical analysis of stochastic dynamical systems and their numerical approximations grouped into four classes:

Stochastic partial differential equations, in particular the Zakai and the Kushner Stratonovitch equation. These stochastic PDEs govern the evolution of the solution of the continuous time stochastic filtering problem.

Partially observed Markov chains. These dynamical systems are related to the discrete time filtering problem. My results cover necessary and sufficient for the convergence of particle approximation to the solution of the filtering problem, optimal algorithms and the stability of the partially observed Markov chains.

Stochastic differential equations, in particular equations perturbed by degenerate noise and their applications to option pricing.

Forward-backward stochastic differential equations and their applications to nonlinear option pricing.

General research interests: Nonlinear Filtering, FBSDEs, Mathematical Finance, Particle Approximations, Malliavin Calculus, Stochastic Partial Differential Equations

Visit Prof Crisan's webpage

E-mail
Phone: (+44) (0)20 7594 8489

Gandy
 

Dr Axel Gandy

- Statistics in Finance/Business
- Computational Statistics, especially adaptive algorithms
- Survival Analysis/Event History Analysis
- Reliability

Visit Dr Gandy's webpage
E-mail
Phone: (+44) (0)20 7594 8518

 Dr Blanka Hovarth

Dr Blanka Hovarth

Blanka is a Postdoctoral Fellow in the Department of Mathematics at Imperial College London. Her research interests are in the area of Stochastic Analysis and Mathematical Finance.

Her interests include asymptotic and numerical methods for option pricing, smile asymptotics for local- and stochastic volatility models (the SABR model and fractional volatility models in particular), Laplace methods on Wiener space and heat kernel expansions.

Visit Dr Hovarth's webpage
Email

Jacquier

Dr Antoine Jacquier

Antoine's research mainly focuses on the study of the asymptotic behaviour of stochastic processes.

He has in particular tackled the following issues:
 
• Closed-form representation of the large-time behaviour of affine processes;
• Small-noise expansions of densities of projected diffusion processes;
• Use of asymptotic methods for robust pricing and calibration of financial derivatives;

General research interests: Large deviations, Implied vo latility, Asymptotic methods, Laplace methods on Wiener space, Mathematical Finance

Visit Dr Jacquier's webpage
E-mail
Phone: (+44) (0)20 7594 8569

Kantas
 

Dr Nikolas Kantas

Nikolas's research interests are concerned with using simulation based methods for inference and optimisation problems.
He focuses mainly on Sequential Monte Carlo and Markov Chain Monte Carlo techniques when applied as computational methods for
- non-linear filtering
- estimation of model parameters for general state space models
- stochastic optimal control
- rare events estimation
- inverse problems and data assimilation

Visit Dr Kantas' webpage
E-mail
Phone: (+44) (0)20 7594 2772

Mijatovic

Dr Aleksandar Mijatovic

Probability and Stochastic processes: martingale theory, SDEs and p rocesses with jumps.

Inference, calibration and simulation for continuous-time stochastic processes.

Visit Dr Mijatovic's webpage
E-mail
Phone: (+44) (0)20 7594 8532

Mikko Pakkenan

Dr Mikko Pakkanen

Mikko's research involves applied probability and stochastic processes, with applications to statistical methods and mathematical finance. In particular, he is interested in:

Mathematical Finance: market microstructure, modelling of limit order books, stochastic volatility models, transaction costs.

Probability: ambit stochastics, central and non-central limit theorems, discretisation of stochastic processes, random fields, support theorems.

Statistics: realised volatility, statistical inference for stochastic processes and random fields.

Visit Dr Pakkanen's webpage
Email
Phone: TBC

Pavliotis

Dr Greg Pavliotis

Greg's research lies in the areas of stochastic processes and statistical mechanics. Currently he is working on the following problems:

• analysis and numerics for stochastic differential equations - Long time asymptotics for hypoelliptic diffusions, amplitude equations for stochastic PDEs, averaging/homogenization for SDEs, numerical analysis for  Stochastic PDEs with multiple scales,

• statistical inference for diffusion processes -Parametric and non-parametric maximum likelihood estimation for multiscale diffusions, Markov Chain Monte Carlo for nonreversible diffusions,

• statistical mechanics - Transport and kinetic theory,  non-equilibrium statistical mechanics, noise-induced transitions, stochastic modeling of Brownian motors.

Visit Dr Pavliotis' webpage
E-mail
Phone: (+44) (0)20 7594 8564

Pistorius

Dr Martijn Pistorius

Martijn's research is concerned with theoretical analysis of random processes, and their numerical realisations. Specific directions are as follows:

• Fluctuation theory; the study of pathwise extrema of a stochastic process. In particular, characterisation of  first-passage times. These arise in various applications, for example the valuation of barrier options. 
• Markov jump-processes; in particular, stochastic differential equations driven by Levy processes, and Markov additive processes. 
• Mathematical finance: Valuation and hedging of derivative securities such as American options; Stochastic volatility modelling. Credit risk valuation.

General research interests: Fluctuation theory, math ematical fin ance, Monte Carlo simulation, stochastic optimal control.


Visit Dr Pistorius' webpage
E-mail
Phone: (+44) (0)20 7594 8532

Veraart

Dr Almut Veraart

Almut's research interests are in statistical methods for stochastic processes, with particular focus on:

• Inference for semimartingales, in particular asymptotic theory based on high frequency data.
• Continuous time modelling of time series, in particular stochastic volatility models.
• Ambit stochastics: Theory of ambit fields and ambit processes with applications to tempo--spatial modelling.
• Applications to Finance, in particular modelling the dynamics of energy prices.

General research interests: Statistica l meth ods for stochastic processes, financial econometrics, applied probability, mathematical finance.

Visit Dr Veraart's webpage
E-mail
Phone: (+44) (0)20 7594 8545

Westray

Dr Nicholas Westray

Visiting Researcher

Research interests:
• algorithmic trading and optimal execution
• market microstructure
• application of stochastic control and statistical methods in algorithmic trading.

E-mail

Associate Members

PhD Students

Student NameSupervisor
Qurat-Ul-Ain Azim Dr Greg Pavliotis
Sergey Badikov Prof Mark Davis / Dr Antoine Jacquier
Richard Bell Dr Martijn Pistorius
Géraldine Bouveret Dr Jean-Francois Chassagneux
Andrea Granelli Dr Almut Veraart / Prof Dan Crisan
Wang Han Prof Dan Crisan
Spyridon Kollias-Liapis Prof Dan Crisan
Sebastian Krumscheid Dr Greg Pavliotis
Kai Li Prof Dan Crisan
Nengli Lim Dr Tom Cass
Hao Liu Dr Antoine Jacquier
Eamon McMurray Prof Dan Crisan
Ivo Mihaylov Dr Jean-Francois Chassagneux / Dr Antoine Jacquier
Francesco Mina Dr Aleksandar Mijatovic
Nicola Pede Prof Damiano Brigo
Patrick Roome Dr Antoine Jacquier
Eric Schaanning Prof Rama Cont
Fangwei Shi MRes Student
Jonnnes Stolte Dr Martijn Pistorius
Sean Violante Prof Dan Crisan
Xun Yang Dr Martijn Pistorius

Visitors

Check back here for infromation about visitors working with the Stochastic Analysis Group at Imperial College

Former Members

Former Members of Stochastic Analysis Group

NameAffiliation
 Christian Litterer  
 Salvador Ortiz-Latorre  University of Oslo
 Konstantinos Manolarakis  
Dr Michela Ottobre  
Dr Yuxin Yang