The course introduces stochastic processes with a view towards applications in fields such as finance, insurance, risk management, and operations research. The aim is to provide mathematics students with basic knowledge of stochastic processes where practical rather than theoretical aspects are emphasized.

Probability Modelling and Applications provides a sound foundation to progress to honours and post-graduate courses emphasizing the theory of mathematical finance and stochastic analysis.

The course contains sufficient material for students to feel comfortable with Markov chains, Poisson processes, and Brownian motion, and the conceptual formulation of topics in continuous time finance, insurance and risk management, where these processes are applied. Also the concept of martingales, which is fundamental for understanding the modern option pricing theory of Black and Scholes, is introduced.

Note: This is an HPC. It continues the development of sophisticated mathematical and probabilistic techniques and their application begun in STAT2001(HPC)

On satisfying the requirements of this course, students will have the knowledge and skills to:

Assessment will be based on:

• Assignments (3) (30%; LO 1-4)
• Tutorials (20%; LO 1-4)
• Final examination (50%; LO 1-4)

STAT2001 or MATH2007.