- Code MATH6115
- Unit Value 6 units
- Offered by Mathematical Sciences Institute
- ANU College ANU Joint Colleges of Science
- Course subject Mathematics
- Areas of interest Mathematics, Theoretical Physics
All activities that form part of this course will be delivered remotely in Sem 2 2020.
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.
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.
- 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]
In response to COVID-19: Please note that Semester 2 Class Summary information (available under the classes tab) is as up to date as possible. Changes to Class Summaries not captured by this publication will be available to enrolled students via Wattle.
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WorkloadThree lectures per week and regular workshops
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 TextsStochastic Calculus and Financial Applicationsby J. Michael Steele. Course notes will also be available to students.
Assumed KnowledgeMeasure theory. Basic concepts and results in probability.
Tuition fees are for the academic year indicated at the top of the page.
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- Student Contribution Band:
- Unit value:
- 6 units
If you are an undergraduate student and 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). You can find your student contribution amount for each course at Fees. Where there is a unit range displayed for this course, not all unit options below may be available.
Offerings, Dates and Class Summary Links
Class summaries, if available, can be accessed by clicking on the View link for the relevant class number.