Dr Giulia Livieri

This course is available on the MSc in Applicable Mathematics, MSc in Econometrics and Mathematical Economics, MSc in Financial Mathematics, MSc in Operations Research & Analytics, MSc in Quantitative Methods for Risk Management, MSc in Statistics, MSc in Statistics (Financial Statistics), MSc in Statistics (Financial Statistics) (Research) and MSc in Statistics (Research). This course is available with permission as an outside option to students on other programmes where regulations permit.

From 2025/26, this course will be compulsory for MSc in Quantitative Methods for Risk Management students.

Students must have completed Stochastic Processes (ST409).

Any student who has not taken ST409 would need to obtain permission from the lecturer. They need to provide a statement explaining the extent to which they have studied topics from ST409 before. If students can demonstrate a good understanding of relevant statistical and machine learning models, this may compensate for ST409, provided the student is ready to acquire the necessary background in probability and stochastic processes through self-study.

The course will equip students with the skills to competently apply modern statistical and machine-learning methods to critical computational problems within the nexus of quantitative finance, risk management, and insurance. The course will start by covering key aspects of Monte Carlo methods, simulation of stochastic processes, and generative adversarial networks with applications to risk management. Next, the course will discuss generalized linear models, building a bridge to deep neural networks and looking at novel applications in insurance. From there, the course proceeds to discuss the key challenges for effective calibration of statistical and machine learning models in general. Finally, the course concludes with a treatment of reinforcement learning and applications to hedging in commodity and energy markets through swing option pricing.

20 hours of lectures and 10 hours of seminars in the WT.

The formative assessment of the course will be based on weekly problem sets given in the seminars/computer classes; the examples in the computer classes will be based both on synthetic (i.e., simulated) and real data examples.

• P. Glasserman, Monte Carlo Methods in Financial Engineering, Springer, 2003
• I. Goodfellow et al., Generative Adversarial Networks, Communications of the ACM, 2020.
• Dobson, A.J.; Barnett, A.G., Introduction to Generalized Linear Models (3rd ed.). 2008.
• A. Bella et. al, Calibration of a Machine Learning model, 2012.
• Sutton, R. and Barto, A., Reinforcement Learning: An Introduction, 1998.

Project (60%) in the WT.
Project (25%, 3500 words) and project (15%, 1000 words) in the ST Week 1.