• Offered by Mathematical Sciences Institute
  • ANU College ANU Joint Colleges of Science
  • Classification Advanced
    Specialist
  • Course subject Mathematics
  • Areas of interest Theoretical Physics
  • Academic career Postgraduate
  • Course convener
    • Dr Pierre Portal
  • Mode of delivery In Person
  • Co-taught Course MATH3015
  • Offered in Second Semester 2018
    See Future Offerings

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.

Learning Outcomes

Upon successful completion of this course, students will have the knowledge and skills to:

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 Assessment

Assignments 25% (LO 1-3)
Mid-Semester Examination 25% (LO 1-3)
Oral presentation 25% (LO 1-3)
Research project 25% (LO 1-3)

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 tutorials

Requisite and Incompatibility

You are not able to enrol in this course if you have completed MATH3015

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.  

If you are a domestic graduate coursework or international student you will be required to pay tuition fees. Tuition fees are indexed annually. Further information for domestic and international students about tuition and other fees can be found at Fees.

Student Contribution Band:
Band 2
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.

Units EFTSL
6.00 0.12500
Domestic fee paying students
Year Fee
2018 $3660
International fee paying students
Year Fee
2018 $5160
Note: Please note that fee information is for current year only.

Offerings and Dates

The list of offerings for future years is indicative only

Second Semester

Class number Class start date Last day to enrol Census date Class end date Mode Of Delivery
7745 23 Jul 2018 30 Jul 2018 31 Aug 2018 26 Oct 2018 In Person

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