LSE: ST552 Probability & Mathematical Statistics I

Lecturers: Dr Giulia Livieri and Prof Umut Cetin

Structure: 20 hours of lectures and 10 hours of seminars (Oct-Dec). Look up timetable here.

Course guide:  https://www.lse.ac.uk/resources/calendar2025-2026/courseGuides/ST/2025_ST552.htm

Sign up: Please email Muhammed Iqbal at M.S.Iqbal@lse.ac.uk (cc'ing lgs.fin.math@gmail.com) stating your name, affiliation, official university email, and PhD supervisor.

Course summary :

This course provides theoretical and axiomatic foundations of probability and mathematical statistics. In particular, the following topics will be covered:

1. Measure spaces; Caratheodory extension theorem; Borel-Cantelli lemmas.

2. Random variables; monotone-class theorem; different kinds of convergence.

3. Kolmogorov’s 0-1 law; construction of Lebesgue integral.

4. Monotone convergence theorem; Fatou's lemmas; dominated convergence theorem.

5. Expectation; L^p spaces; uniform integrability.

6. Characteristic functions; Levy inversion formula; Levy convergence theorem; CLT.

7. Principle and basis for statistical inference: populations and samples, decision theory, basic measures for estimators.

8. Estimation: U and V statistics, unbiased estimators, MVUE, MLE.

9. Hypothesis testing: Neyman-Pearson lemma, UMP, confidence sets.

10. Product measures; conditional expectation.

Imperial College: MSc in Mathematics and Finance

There are a limited number of places available to LMF students on the modules of the Imperial College MSc in Mathematics and Finance.

The following rules apply:

• No marking or grading of coursework or exam will be provided
• The lecturer and/or the Co-Director may refuse candidates (e.g., if not enough spaces, lack of prerequisites, or other reasons)

Sign up:  Please   email the course lecturer, cc'ing the Co-Director Eyal Neuman (e.neumann@imperial.ac.uk)

Courses in Term 1, 2025 (27 Sep– 12 Dec):

Core Modules (Weeks 2-11 of term):

• MATH70107 Fundamentals of Option Pricing (Dr Zheng)
• MATH70108 Statistical Methods in Finance (Prof. Cass)
• MATH70109 Stochastic Processes (Dr Neuman)
• MATH70110 Quantitative Risk Management (Prof. Zheng & Dr Coache)
• MATH70112 Computing for Finance - Python (Dr Muguruza)
  
  

Elective Modules (15 hours):

• MATH70118 Quantum Machine Learning in Finance (Dr Kondratyev) — Weeks 7-11 of term
• MATH70116 Deep Learning (Dr Gonon) — Weeks 2-6 of term
• MATH70129 Portfolio Management (Dr Yifan Jiang) — Weeks 2-6 of term
• MATH70122 Optimisation in Machine Learning (Dr Coache) — Weeks 7-11 of term