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
S1-FF-CLAYTON-FLEXIBLE

Rules

Enrolment Rule

Contacts

Chief Examiner(s)

Dr Andrea Collevecchio

Unit Coordinator(s)

Dr 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 summary

Examination (3 hours and 10 minutes): 60% (Hurdle)

Continuous assessment: 40%

Hurdle requirement: If you would otherwise have passed the unit but who do not achieve at least 45% of the marks available for the end-of-semester examination will receive a Hurdle Fail (NH) grade and a mark of 45 on your transcript.

Workload requirements

Workload

Other unit costs

Costs are indicative and subject to change.
Miscellaneous items required (Printing, Stationery)- $100.