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
3 hour Written Unseen Examination (80%); In-course Assessment (20%)