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Mathematical Sciences Institute · ANU College of Systems and Society
This course gives a rigorous mathematical introduction to stochastic processes, stochastic differential equations, and their applications in finance. The first half of the course covers martingales, Poisson processes, Brownian motion, Ito integration, and stochastic differential equations driven by a Brownian motion. The second half of the course covers a range of more advanced topics to be selected by the students. This includes option pricing and investment optimisation, basics of Malliavin's stochastic calculus of variations, Black-Scholes formula and hedging, as well as aspects of the relationship between stochastic analysis and partial differential equations. Stochastic Analysis with Financial Applications provides an accessible but mathematically rigorous introduction to financial mathematics and quantitative finance. This course is co-taught with undergraduate students but assessed separately. Assessment will include a research project.
Assignments
Learning outcomes 1, 2, 3
Mid-Semester Examination
Learning outcomes 1, 2, 3
Oral presentation
Learning outcomes 1, 2, 3, 4
Research Project
Learning outcomes 1, 2, 3, 4
The expected workload will consist of approximately 130 hours throughout the semester. The course operates as a flipped classroom. This means that students first learn the content before meeting with the lecturer, and then they use the in-person class time to reach a deep level of understanding. In practice, this means the expected workload is: • Approximately 82 hours of self-directed study which will include: - watching approximately 33 pre-recorded videos and reading lecture notes covering the course content, to prepare for the in-person activities in Weeks 1 to 10, - preparation for assessment tasks, and - watching through other students' oral presentation videos in preparation for the discussions of them in Weeks 11 and 12; • Face-to face component which will consist of approximately 48 hours of scheduled in-person activities during the semester. These in-person activities will include a 1 hour workshop most weeks plus up to 3 hours per week of other in person activities (detail in the class summary).
There is no prescribed textbook. Extensive lecture notes are provided. Preliminary Reading "Stochastic calculus and financial applications" by M. Steele (ISBN 978-1-4684-9305-4) is highly recommended.