MTH5220 · The theory of martingales in discrete time

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

Assessment

The Handbook lists an examination for this unit.

Assessment details may change. Please refer to the assessment information in Moodle closer to the start of the teaching period.

Requisites

The Handbook lists no prerequisite, corequisite or prohibition for this unit.

Learning outcomes

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.

Workload

• Two 1.5-hour seminars; • One 1-hour applied class (in weeks 2-12) and • 8 hours of independent study per week.

Student experience, not official rules. Nothing here changes what the Handbook says.