Module Title  LM Stochastic Processes 
School  Mathematics 
Department  Mathematics 
Module Code  06 36976 
Module Lead  Dr Nikolaos Fountoulakis 
Level  Masters Level 
Credits  20 
Semester  Semester 1 
Prerequisites 

Corequisites 

Restrictions  Level M MSci students are expected to have passed 2S/2S3 Statistics (25671/27147)
There are no prerequisites for MSc students, since they are expected at the programme level to have the appropriate background. 
Contact Hours 
Lecture44 hours
Practical Classes and workshops10 hours
Guided independent study146 hours
Total: 200 hours

Exclusions  
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 
3697601 : Raw Module Mark : Coursework (100%)

Assessment Methods & Exceptions  "Assessment:
20% incourse assessment (via two online open book class tests) and 80% via either an oncampus examination or an openbook online alternative assessment
Reassessment:
There are no reassessment 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%." 
Other  
Reading List 
