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. The course provides a sound foundation for progress to honours and post-graduate courses in these or related areas.
Note: This is an Honours Pathway Course. It continues the development of sophisticated mathematical techniques and their application begun in MATH3029 or MATH3320.
Learning Outcomes
Upon successful completion, students will have the knowledge and skills to:
- Explain the core mathematical tools and fundamental concepts of modern financial mathematics;
- Use stochastic calculus in mathematical and financial problems, including option pricing;
- Demonstrate capabilities for advanced mathematical reasoning, analysis, and modeling linked to the theory of stochastic processes.
Indicative Assessment
- Regular written assignments (25) [LO 1,2,3]
- Mid-semester examination (25) [LO 1,2,3]
- Pre-recorded oral presentation (25) [LO 1,2,3]
- Final essay (25) [LO 1,2,3]
The ANU uses Turnitin to enhance student citation and referencing techniques, and to assess assignment submissions as a component of the University's approach to managing Academic Integrity. While the use of Turnitin is not mandatory, the ANU highly recommends Turnitin is used by both teaching staff and students. For additional information regarding Turnitin please visit the ANU Online website.
Workload
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).
Inherent Requirements
No specific inherent requirements have been identified in this course.
Requisite and Incompatibility
Prescribed Texts
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.
Fees
Tuition fees are for the academic year indicated at the top of the page.
Commonwealth Support (CSP) Students
If you have been offered a Commonwealth supported place, your fees are set by the Australian Government for each course. At ANU 1 EFTSL is 48 units (normally 8 x 6-unit courses). More information about your student contribution amount for each course at Fees.
- Student Contribution Band:
- 1
- Unit value:
- 6 units
If you are a domestic graduate coursework student with a Domestic Tuition Fee (DTF) place or international student you will be required to pay course tuition fees (see below). Course tuition fees are indexed annually. Further information for domestic and international students about tuition and other fees can be found at Fees.
Where there is a unit range displayed for this course, not all unit options below may be available.
| Units | EFTSL |
|---|---|
| 6.00 | 0.12500 |
Course fees
- Domestic fee paying students
| Year | Fee |
|---|---|
| 2025 | $4680 |
- International fee paying students
| Year | Fee |
|---|---|
| 2025 | $6720 |
Offerings, Dates and Class Summary Links
ANU utilises MyTimetable to enable students to view the timetable for their enrolled courses, browse, then self-allocate to small teaching activities / tutorials so they can better plan their time. Find out more on the Timetable webpage.
Class summaries, if available, can be accessed by clicking on the View link for the relevant class number.
Second Semester
| Class number | Class start date | Last day to enrol | Census date | Class end date | Mode Of Delivery | Class Summary |
|---|---|---|---|---|---|---|
| 8558 | 21 Jul 2025 | 28 Jul 2025 | 31 Aug 2025 | 24 Oct 2025 | In Person | N/A |