ST552 Probability and Mathematical Statistics I

Lecturer : Dr Giulia Livieri, Professor Kostas Kardaras, Professor Angelos Dassios

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

Link:  https://www.lse.ac.uk/resources/calendar2023-2024/courseGuides/ST/2023_ST552.htm

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 students of the LGS on modules of the Imperial College MSc in Mathematics and Finance. Below is a list of all autumn courses and the following rules apply:

• Interested PhD students should email the corresponding lecturer (as mentioned in parenthesis after the course title below) 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 Course Director may refuse some candidates (if not enough spaces, lack of prerequisites, or other reasons)

Core Modules:

• Fundamentals of Option Pricing (Dr Siorpaes) MATH70107
• Statistical Methods for Finance (Dr Salvi) MATH70108
• Stochastic Processes (Dr Neuman) MATH70109
• Quantitative Risk Management (Dr Gonon) MATH70110
• Computing for Finance - Python (Dr Muguruza) MATH70112 (Weeks 2-11)
  
  

Elective Modules:

• Data Science for Fintech, Regtech, Suptech (Dr Cambe) MATH70117 (Weeks 2-6)
• Quantum Computing (Dr Jacquier, Dr Kondratyev) MATH70118 (Weeks 7-11)
• Deep Learning (Dr Gonon) MATH70116 (Weeks 2-11 once every 2 weeks)
• Portfolio Management (Dr Bonesini) MATH70129 (Weeks 7-11)