Courses
Winter 2025
ST553 Probability and Mathematical Statistics II
Lecturer: Prof Konstantinos Kardaras
Time, dates and location: 20 hours of lectures and 10 hours of seminars (click here for dates and times)
Link: https://www.lse.ac.uk/resources/calendar2024-2025/courseGuides/ST/2024_ST553.htm
Prerequisites:
Probability and Mathematical Statistics I (or equivalent) is a pre-requisite.
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 College: 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 Autumn 2024:
Core Modules (Weeks 2-6):
- Computing for Finance- C++ (Dr Bilokon) MATH70112
- Interest Rate Models with Credit Risk, Collateral, Funding Liquidity Risk and Multiple Curves (Prof Brigo & Dr Zhang) MATH70111
- Simulation Methods for Finance (Dr Zhang) 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)
- Rough Paths and Signatures in Machine Learning (Dr Salvi) MATH70124 (Weeks 2-6)
- 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 (Prof. Jacquier & Dr Lucic) MATH70128 (Weeks 7-11)