6 points, SCA Band 2, 0.125 EFTSL
Postgraduate - Unit
Refer to the specific census and withdrawal dates for the semester(s) in which this unit is offered.
Faculty
Organisational Unit
School of Mathematical Sciences
Chief examiner(s)
Coordinator(s)
Unit guides
Prerequisites
MTH3241 (or equivalent)
Co-requisites
Only students enrolled in the Master of Financial Mathematics can enrol in this unit. Exceptions can be made with permission from the unit co-ordinator.
Synopsis
Doob's convergence theorem. Optional sampling theorem. Discrete Stochastic integral. Martingale inequalities such as Doob and Burkholder-Davis-Gundy inequalities. Bucy-Kalman filter. Applications to finance. Option pricing - discrete Black-Scholes formula. Control theory.
Outcomes
On completion of this unit students will be able to:
- Develop specialised mathematical knowledge and skills within the theory of martingales.
- Apply sophisticated stochastic modelling skills within a variety of contexts, from population biology to finance to management science, and more.
- Apply critical thinking to problems in discrete-time stochastic processes in general, and in the theory of discrete-time martingales in particular.
- Formulate expert solutions to practical financial, engineering or scientific problems using specialised cognitive and technical skills within the theory of discrete-time martingales.
Assessment
Examination (3 hours): 60% (Hurdle)
Continuous assessment: 40%
Hurdle requirement: To pass this unit a student must achieve at least 50% overall and at least 40% for the end-of-semester exam.
Workload requirements
Two 1.5 -hour lectures and one 1-hour tutorial per week
See also Unit timetable information