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.
Learning Outcomes
Upon successful completion, students will have the knowledge and skills to:
- Demonstrate a deep understanding of the core mathematical tools and fundamental concepts of modern financial mathematics;
- Use stochastic calculus efficiently in mathematical and financial problems, including option pricing;
- Demonstrate strong capabilities for advanced mathematical reasoning, analysis and modeling linked to the theory of stochastic processes.
Indicative Assessment
- Assignments (25) [LO 1,2,3]
- Mid-Semester Examination (25) [LO 1,2,3]
- Oral presentation (25) [LO 1,2,3]
- Research project (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
Three lectures per week and regular workshopsInherent Requirements
To be determined
Requisite and Incompatibility
You will need to contact the Mathematical Sciences Institute to request a permission code to enrol in this course.
Prescribed Texts
Stochastic Calculus and Financial Applicationsby J. Michael Steele. Course notes will also be available to students.Assumed Knowledge
Measure theory. Basic concepts and results in probability.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 |
|---|---|
| 2023 | $4320 |
- International fee paying students
| Year | Fee |
|---|---|
| 2023 | $6180 |
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 |
|---|---|---|---|---|---|---|
| 5958 | 24 Jul 2023 | 31 Jul 2023 | 31 Aug 2023 | 27 Oct 2023 | In Person | N/A |
