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:

1. Explain the fundamental concepts of probability theory and its position in modern mathematics and applied contexts;
2. Demonstrate accurate and efficient use of probability theory techniques;
3. Demonstrate capacity for mathematical reasoning through analyzing, proving and explaining concepts from probability theory;
4. Apply problem-solving using probabilistic methods in various situations in mathematical finance.

Assessment will be based on:

• Weekly Assignments (50%; LO 1-4)
• Final examination (50%; LO 1-4)

This course will only be offered subject to staff availability

STAT2001 or MATH2320 or MATH3116.