Programme And Module Handbook
Course Details in 2025/26 Session

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Module Title LM Stochastic Processes
Department Mathematics
Module Code 06 36976
Module Lead Dr Nikolaos Fountoulakis
Level Masters Level
Credits 20
Semester Semester 1
Restrictions Level M MSci students are expected to have passed 2S/2S3 Statistics (25671/27147)

There are no pre-requisites for MSc students, since they are expected at the programme level to have the appropriate background.
Contact Hours Lecture-44 hours
Practical Classes and workshops-10 hours
Guided independent study-146 hours
Total: 200 hours
Description This an introductory module into Stochastic Processes appropriate to final year undergraduate students and postgraduate students. While students will be exposed to the relative mathematical theorems there will be an emphasis on the understanding of the relevant definitions and on the application of the underlying results. The module begins with a thorough introduction to the properties of Stochastic processes, followed by a discussion of Markov processes, discrete and continuous Martingales, Brownian Motion and Gaussian process. Stochastic Calculus is introduced and Itô’s formula is used to derive the Black Scholes Equation of Mathematical Finance.
Learning Outcomes By the end of the module students should be able to:
  • Explain the key features of stochastic processes and demonstrate a strong understanding of Markov processes.
  • Understand and explore both discrete and continuous Martingales
  • Model processes governed by Brownian Motion and Gaussian process
  • Perform applications from Stochastic Calculus including the derivation of the Black Scholes Equations.
Assessment 36976-01 : Raw Module Mark : Coursework (100%)
Assessment Methods & Exceptions "Assessment: 20% in-course assessment (via two online open book class tests) and 80% via either an on-campus examination or an open-book online alternative assessment Reassessment: There are no re-assessment opportunities for MSci Students. MSc students will be allowed a second and final attempt at the final examination during the Supplementary examination period with their final mark capped at the pass level of 50%."
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