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/calendar2023-2024/courseGuides/ST/2023_ST553.htm

Prerequisites: 

Probability and Mathematical Statistics I 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 is a limited number of places available to students of the LGS on modules of the Imperial College MSc in Mathematics and Finance. Below is a list of all spring courses and the following rules apply:

Interested PhD students should email the corresponding lecturer(s) and cc Eyal Neumann (e.neumann@imperial.ac.uk) to ask for approval. Not that:

• No marking or grading of coursework or exam will be provided
• The lecturer or the Course Director may refuse some candidates (if too many or other reasons)

Core Modules :

Computing for Finance- C++ (Dr Bilokon) MATH70112
Interest Rate Models with Credit Risk, Collateral, Funding Liquidity Risk and Multiple

Curves (Prof. Brigo) MATH70111
Simulation Methods for Finance (Dr Zhang) MATH70113

Elective Modules:

Numerical Methods in Finance (Dr Stockinger) MATH70119 (Weeks 2-6)

Convex Optimisation (Dr Shadmi) MATH70122 (Weeks 2-6)
Advances in Machine Learning (Dr Bilokon) MATH70120 (Weeks 2-6)
Topics in Derivatives Pricing (Dr Piterbarg) MATH70121 (Weeks 2-6)
Rough Paths and Signatures in Machine Learning (Dr Salvi) MATH70124 (Weeks 7-11)
Market Microstructure (Prof. Rosenbaum) MATH70125 (Weeks 2-6)
Stochastic Control in Finance (Dr Itkin) MATH70126 (Weeks 2-6)

Quantitative Trading and Price Impact (Prof. Muhle-Karbe, Dr Webster) MATH70127 (Weeks 7-11)
Topics in Quantitative Finance (Dr Jacquier, Dr Lucic) MATH70128 (Weeks 7-11)