Registry
Module Specifications
Current Academic Year 2012 - 2013
Please note that this information is subject to change.
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| Description | |||||||||||||||||||||||||||||||||||||||||||||
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This module provides a self-contained treatment of the theory of expectation (integration) and conditional expectation. While no prior knowledge of these topics is assumed , some familiarity with abstract mathematical reasoning is expected . The modules contains also a brief introduction to discrete-time Martingales concentating on their role in the theory of discrete-time finance. No prior knowledge of finance is assumed . This is primarily a "knowledge" type module | |||||||||||||||||||||||||||||||||||||||||||||
| Learning Outcomes | |||||||||||||||||||||||||||||||||||||||||||||
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1. State the main definitions relevant to advanced probability and asset pricing and demonstrate an understanding of these through examples and counter-examples 2. Prove the main theorems of expectation theory 3. Derive the main properties of conditional expectations from their geometric characterisation 4. Apply martingales and arbitrage methods to discrete-time financial models 5. Demonstrate an understanding of the method of pricing by replication by proving selected results of the theory of options | |||||||||||||||||||||||||||||||||||||||||||||
All module information is indicative and subject to change. For further information,students are advised to refer to the University's Marks and Standards and Programme Specific Regulations at: http://www.dcu.ie/registry/examinations/index.shtml |
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| Indicative Content and Learning Activities | |||||||||||||||||||||||||||||||||||||||||||||
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Events. probability triple, elementary approach, general sample space, Axioms, sigma algebras,probability measures, necessity of axiomatic construction, Borel sigma algebra, extension of probabilities.. Random Variables. measurability, elementary properties, limit of sequences of random variables, probability distribution functions.. Expectation. simple random variables, approximation of positive r.v.s by simple ones, expectation as an integral over the sample space; the main limit theorems: monotone convergence, dominated convergence .. Conditional Expectation. elementary definition, conditional expectation with respect to a decomposition of the sample space; conditional expectation with respect to a sub sigma algebra as an orthogonal projection; martingales.. Models of the Stock Market. simple binomial model: options, pricing a call by replication; general model: trading strategies, arbitrage, replicating portfolio, complete and incomplete markets.The two fundamental theorems of asset pricing.. | |||||||||||||||||||||||||||||||||||||||||||||
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| Indicative Reading List | |||||||||||||||||||||||||||||||||||||||||||||
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| Other Resources | |||||||||||||||||||||||||||||||||||||||||||||
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| Programme or List of Programmes | |||||||||||||||||||||||||||||||||||||||||||||
| MFM | MSc in Financial Mathematics | ||||||||||||||||||||||||||||||||||||||||||||
| Timetable this semester: Timetable for MS407M | |||||||||||||||||||||||||||||||||||||||||||||
| Date of Last Revision | 18-JUN-08 | ||||||||||||||||||||||||||||||||||||||||||||
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