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Module Title
LM Stochastic Processes
School
Mathematics
Department
Mathematics
Module Code
06 37788
Module Lead
Level
Masters Level
Credits
20
Semester
Semester 1
Pre-requisites
Co-requisites
Restrictions
None
Exclusions
Description
This module forms an introduction to Stochastic Processes. 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 Ito'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:
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.
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%.
