Unit name | Martingale Theory with Applications 4 |
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Unit code | MATHM6204 |

Credit points | 10 |

Level of study | M/7 |

Teaching block(s) |
Teaching Block 1 (weeks 1 - 12) |

Unit director | Professor. Balint Toth |

Open unit status | Not open |

Pre-requisites |
MATH21400 Applied Probability 2 |

Co-requisites |
None |

School/department | School of Mathematics |

Faculty | Faculty of Science |

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.

General Description of the Unit

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

Applied 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 post-graduate 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 (MATH35400), Further Topics in Probability 3 (MATH30006) and Introduction to Stochastic Analysis (MATHM0017).

Compared to the level 3 version of this unit, the level M version has the additional requirement of directed self study based on read paper(s) in areas of current research interest and submitting a written report, thus students in the level M unit will gain a more in-depth undertanding of the power of the martingale approach.

Further information is available on the School of Mathematics website: http://www.maths.bris.ac.uk/study/undergrad/

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. Better ability to learn material by directed reading.

Lectures and homework assignments. Bi-weekly assignments to be done by the student and handed in for marking. Self-study with directed reading of research papers.

80% Examination and 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.

Williams, D., Probability with Martingales (CUP).