- Code MATH6115
- Unit Value 6 units
- Offered by Mathematical Sciences Institute
- ANU College ANU Joint Colleges of Science
- Course subject Mathematics
- Areas of interest Theoretical Physics
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.
Mathematics of Finance 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.
Upon successful completion, students will have the knowledge and skills to:
successful completion of this course, students will have the knowledge and
1. Demonstrate a deep understanding of the core mathematical tools and fundamental concepts of modern financial mathematics;
2. Use stochastic calculus efficiently in mathematical and financial problems, including option pricing;
3. Demonstrate strong capabilities for advanced mathematical reasoning, analysis and modeling linked to the theory of stochastic processes.
Indicative AssessmentAssignments 25% (LO 1-3)
Mid-Semester Examination 25% (LO 1-3)
Oral presentation 25% (LO 1-3)
Research project 25% (LO 1-3)
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WorkloadThree lectures per week and regular workshops
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.