UNIVERSITY OF KENT
MODULE SPECIFICATION
SECTION 1: MODULE SPECIFICATIONS
1.
Title of the module: Probability and Measure Theory (MA518)
2.
School or partner institution which will be responsible for management of the module
School of Mathematics, Statistics and Actuarial Science
3.
Start date of the module: September 2014
4.
The number of students expected to take the module: 50 (2014/15)
5.
Modules to be withdrawn on the introduction of this proposed module and consultation with other
relevant Schools and Faculties regarding the withdrawal
None.
6.
The level of the module (e.g. Certificate [C], Intermediate [I], Honours [H] or Postgraduate [M]): I
7.
The number of credits and the ECTS value which the module represents : 15 (ECTS 7.5)
8.
Which term(s) the module is to be taught in (or other teaching pattern): Spring term
9.
Prerequisite and co-requisite modules:
Prerequisite modules: MA306 Statistics and MA312 Introduction to Financial Concepts
There are no co-requisite modules.
10. The programmes of study to which the module contributes
BSc (Hons) Financial Mathematics (including programme with a year in industry)
11. The intended subject specific learning outcomes
On successful completion of this module students will be able to:
a) work with the basic tools of measure theory such as measurable functions, sigma-fields and
filtrations;
b) use correctly the concept of conditional expectation;
c) use martingale sequences in discrete and continuous time;
d) apply the above skills in a financial context.
12. The intended generic learning outcomes
Students who successfully complete this module will:
a) develop a logical mathematical approach to solving problems;
b) be able to work independently to apply techniques learnt in one context in other contexts.
13. A synopsis of the curriculum
Sigma-fields, Measurable Spaces, Measurable Functions, definition of a measure, probability
measure, Borel set, Lesbesgue measure, Lesbesgue integration, Radon-Nikodym Theorem,
filtrations, Conditional Expectation and its properties. Discrete and Continuous martingales.
Applications of Measure Theory in Stochastic Modeling and Finance.
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UNIVERSITY OF KENT
14. Indicative Reading List
Resnick, Sidney, A Probability Path, 2003, Birkhauser
Williams, David, Probability with Martingales, 1991, Cambridge University Press
Klenke, Akin, Probability Theory: a comprehensive course, 2014, Springer
15. Learning and Teaching Methods, including the nature and number of contact hours and the total
study hours which will be expected of students, and how these relate to achievement of the intended
module learning outcomes.
No of contact hours: 48 (48 lectures/ example classes/supervised problem solving sessions)
Independent study hours: 102
Total study hours: 150
Teaching methods will comprise a mix of lectures and example classes/supervised problem solving
sessions. Subject specific learning outcomes 11(a)-(d) and generic learning outcomes 12(a),(b) will
be addressed by the lectures and classes/problem solving sessions. Generic learning outcome 12(b)
will be developed by work on the coursework assessments.
16. Assessment methods and how these relate to testing achievement of the intended module learning
outcomes
This module is assessed by coursework (20%) and by examination (80%).
Coursework: This will normally consist of class tests and/or open-book written assignments mostly
completed by students outside contact hours (assessing learning outcomes 11(a)-(d) and 12(a),(b)).
Examination: A 2-hour unseen written examination in the Summer Term that consists of a mix of
short and long answers that test to varying levels of proficiency learning outcomes 11(a)-(d) and
12(a),(b).
17. Implications for learning resources, including staff, library, IT and space
The module has been designed as a dedicated module for the BSc in Financial Mathematics. Extra
teaching resources required for the module will be met within the Statistics group of the School.
Relevant books and other reading material will be made available in the library and the university
bookshop. There are not expected to be any additional IT or Library resource requirements.
18. The School recognises and has embedded the expectations of current disability equality legislation,
and supports students with a declared disability or special educational need in its teaching. Within
this module we will make reasonable adjustments wherever necessary, including additional or
substitute materials, teaching modes or assessment methods for students who have declared and
discussed their learning support needs. Arrangements for students with declared disabilities will be
made on an individual basis, in consultation with the University’s disability/dyslexia support service,
and specialist support will be provided where needed.
19. Campus where module will be delivered: Canterbury
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UNIVERSITY OF KENT
SECTION 2: MODULE IS PART OF A PROGRAMME OF STUDY IN A UNIVERSITY SCHOOL
Statement by the School Director of Learning and Teaching/School Director of Graduate Studies
(as appropriate): "I confirm I have been consulted on the above module proposal and have given advice
on the correct procedures and required content of module proposals"
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Director of Learning and Teaching/Director of
Graduate Studies (delete as applicable)
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Date
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Print Name
Statement by the Head of School: "I confirm that the School has approved the introduction of the
module and, where the module is proposed by School staff, will be responsible for its resourcing"
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Head of School
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Date
…………………………………………………….
Print Name
Module Specification Template
Last updated February 2013
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