Overview
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.
Offerings
S1-01-CLAYTON-ON-CAMPUS
Rules
Enrolment Rule
Contacts
Chief Examiner(s)
Associate Professor Andrea Collevecchio
Unit Coordinator(s)
Associate Professor Andrea Collevecchio
Learning outcomes
On successful completion of this unit, you should be able to:
1.
Develop specialised mathematical knowledge and skills within the theory of martingales.
2.
Apply sophisticated stochastic modelling skills within a variety of contexts, from population biology to finance to management science, and more.
3.
Apply critical thinking to problems in discrete-time stochastic processes in general, and in the theory of discrete-time martingales in particular.
4.
Formulate expert solutions to practical financial, engineering or scientific problems using specialised cognitive and technical skills within the theory of discrete-time martingales.
Assessment
1 - Continuous assessment
2 - Final assessment - Exam (3 hours and 10 minutes)
Scheduled and non-scheduled teaching activities
Applied sessions
Seminars
Workload requirements
Workload
Other unit costs
Costs are indicative and subject to change.
Miscellaneous items required (printing, stationery)- $100.