This unit entry is for students who completed this unit in 2016 only. For students planning to study the unit, please refer to the unit indexes in the the current edition of the Handbook. If you have any queries contact the managing faculty for your course or area of study.

MTH5220 - The theory of martingales in discrete time

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

Science

Organisational Unit

School of Mathematical Sciences

Coordinator(s)

Dr Andrea Collevecchio

Offered

Clayton

First semester 2016 (Day)

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

Weekly homework: 15%
Assignments: 15%
Exam: 70%

Workload requirements

Two 1.5 -hour lectures and one 1-hour tutorial per week

Chief examiner(s)

Dr Andrea Collevecchio

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.