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Unit information: Martingale Theory with Applications 3 in 2019/20

Please note: Due to alternative arrangements for teaching and assessment in place from 18 March 2020 to mitigate against the restrictions in place due to COVID-19, information shown for 2019/20 may not always be accurate.

Please note: you are viewing unit and programme information for a past academic year. Please see the current academic year for up to date information.

Unit name Martingale Theory with Applications 3
Unit code MATH36204
Credit points 10
Level of study H/6
Teaching block(s) Teaching Block 1A (weeks 1 - 6)
Unit director Dr. Balazs
Open unit status Not open
Pre-requisites

MATH20008 Probability 2

Co-requisites

None

School/department School of Mathematics
Faculty 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

Lectures and homework assignments. Bi-weekly assignments to be done by the student and handed in for marking.

Assessment Details

80% 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.

Reading and References

Recommended

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

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