LSE: ST553 Probability and Mathematical Statistics II

Lecturer:  Prof Kostas Kardaras

Time, dates and location:  20 hours of lectures and 10 hours of seminars (click here for the timetable)

Link:  https://www.lse.ac.uk/resources/calendar/courseGuides/ST/2025_ST453.htm

Prerequisites: 

ST552 Probability and Mathematical Statistics I or equivalent preparation.

Course summary:

This course provides instruction in advanced topics in probability and mathematical statistics, mainly based on martingale theory. It is a continuation of Probability and Mathematical Statistics I. The following topics will in particular be covered:

Conditional expectation revisited; linear regression; martingales and first examples.

Concentration inequalities; dimension reduction; log-Sobolev inequalities.

Martingale transforms; optional sampling theorem; convergence theorems.

Sequential testing; backwards martingales; law of large numbers; de Finetti’s theorem.

Markov chains; recurrence; reversibility; foundations of MCMC.

Ergodic theory.

Brownian motion; quadratic variation; stochastic integration.

Stochastic differential equations; diffusions; filtering.

Bayesian updating; Ergodic diffusions; Langevin samplers.

Brownian bridge; empirical processes; Kolmogorov-Smirnov statistic.

Imperial: MSc in Mathematics and Finance

There are a limited number  of places available to students of the LGS on modules of the Imperial College MSc in Mathematics and Finance. The following rules apply:

• Interested PhD students should email the course lecturer and cc the Co-Director Eyal Neuman (e.neumann@imperial.ac.uk) for approval
• No marking or grading of coursework or exam will be provided
• The lecturer or the Co-Director may refuse candidates (e.g., if not enough spaces, lack of prerequisites, or other reasons)

Courses available in Winter 2026 (Jan-March):

Core Modules (Weeks 2-6):

• Computing for Finance- C++ (Dr Bilokon) MATH70112
• Interest Rate Models  (Prof Brigo & Dr Zhang) MATH70111
• Simulation Methods for Finance (Dr Tse & Dr Jiang) MATH70113

Elective Modules:

• Numerical Methods in Finance (Dr Jettkant) MATH70119 (Weeks 2-6)
• Advances in Machine Learning (Dr Zhang) MATH70120 (Weeks 2-6)
• Topics in Derivatives Pricing (Dr Piterbarg) MATH70121 (Weeks 7-11)
• Market Microstructure (Prof Rosenbaum) MATH70125 (Weeks 2-6)
• Stochastic Control in Finance (Prof. Zheng) MATH70126 (Weeks 2-6)
• Quantitative Trading and Price Impact (Prof. Muhle-Karbe) MATH70127 (Weeks 7-11)
• Topics in Quantitative Finance (Dr Lucic) MATH70128 (Weeks 7-11)
• Generative Modelling in Finance (Dr Salvi) MATH70065