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| Module Availability |
Spring Semester
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| Assessment Pattern |
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Unit(s) of Assessment
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Weighting Towards Module Mark( %)
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Coursework: the form of exercises and class tests
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25%
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Exam: Written examination (2 hours, unseen).
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75%
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| Module Overview |
| The module introduces Brownian motion, related continuous time, continuous state space stochastic processes and processes with independent and stationary increments. |
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| Prerequisites/Co-requisites |
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Prerequisite: MAT2003 Stochastic Processes
Recommended: MAT2013 Mathematical Statistics
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| Module Aims |
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| Learning Outcomes |
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At the end of the module a student should be able to:
(1) define Brownian motion and related processes and calculate associated probabilities
(2) construct and analyse processes with independent and stationary increments
define and apply martingales in continuous time.
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| Module Content |
Continuous time and state space models. Brownian motion, reflection principle, relation to random walks. General Gauss-Wiener process, Ornstein-Uhlenbeck process, multivariate Wiener process, lognormal Wiener process. Processes with independent and stationary increments: Levy processes and stable laws. Martingales, filtrations, stopping times. |
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| Methods of Teaching/Learning |
3 contact hours per week for 10 weeks. Teaching is by lectures and tutorials. Learning takes place through lectures, tutorials, exercises and background reading. |
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| Selected Texts/Journals |
Recommended
H M Taylor and S. Karlin, An introduction to stochastic modelling, 3rd ed, Academic Press, (1998)
Further Reading
G R Grimmett and D Stirzaker, Probability and Random Processes, 2nd ed, Clarendon 1992
R S Pindyck and D L Rubinfeld, Econometric Models and Economic Forecasts, McGraw-Hill (1998)
Core Reading for Subject 103, Institute and Faculty of Actuaries (1999). |
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| Last Updated |
10 October 2008 |
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