# Unit information: Martingale Theory with Applications 3 in 2020/21

Unit name Martingale Theory with Applications 3 MATH36204 10 H/6 Teaching Block 1A (weeks 1 - 6) Dr. Balazs Not open MATH20008 Probability 2 None School of Mathematics Faculty of Science

## Description

Unit Aims

To stimulate through theory and examples, an interest and appreciation of the power of this elegant method in probability theory. And to lay foundations for further studies in probability theory.

Unit Description

The theory of martingales is of fundamental importance to probability theory, statistics, and mathematical finance. This unit is a concise introduction of the basic concepts, results and examples of this powerful and elegant theory.

Relation to Other Units

Probability 2 has introduced Martingales, but only covers the most basic of results, mostly without rigorous proofs. This unit will prove most of the results in a rigorous measure-theoretic fashion, and will be essential for students who wish to go on to study postgraduate level probability theory. In particular, students will find the understanding of material in this unit very helpful in other related units, such as Financial Mathematics and Further Topics in Probability 3.

## Intended learning outcomes

Learning Objectives

To gain an understanding of martingales, and to be able to formulate problems in probability/statistics theory in terms of martingales. Students will also gain more experience in writing proofs, thus laying the foundation for future studies in probability theory at a post-graduate level.

Transferable Skills

Formulation of probability/statistics problems in terms of martingales. Better ability in writing proofs.

## Teaching details

The unit will be taught through a combination of

• synchronous online and, if subsequently possible, face-to-face lectures
• asynchronous online materials, including narrated presentations and worked examples
• guided asynchronous independent activities such as problem sheets and/or other exercises
• synchronous weekly group problem/example classes, workshops and/or tutorials
• synchronous weekly group tutorials
• synchronous weekly office hours

## Assessment Details

80% Timed, open-book examination 20% Coursework

Raw scores on the examinations will be determined according to the marking scheme written on the examination paper. The marking scheme, indicating the maximum score per question, is a guide to the relative weighting of the questions. Raw scores are moderated as described in the Undergraduate Handbook.

If you fail this unit and are required to resit, reassessment is by a written examination in the August/September Resit and Supplementary exam period.

## Reading and References

Recommended

• Albert N. Shyriaev, Probability, Second Edition, Springer, 1996
• David Williams, Probability with Martingales, Cambridge University Press, 1991