Registry

Module Specifications

Current Academic Year 2012 - 2013
Please note that this information is subject to change.

Module Title	Probability and Finance I
Module Code	MS407
School	School of Mathematics
Online Module Resources
Module Co-ordinator	Semester 1: John Appleby Semester 2: John Appleby Autumn: John Appleby
Module Teacher	John Appleby
NFQ level	8	Credit Rating	7.5
Pre-requisite	None
Co-requisite	None
Compatibles	None
Incompatibles	None

Description

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

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

Workload	Full-time hours per semester
*Type*	*Hours*	*Description*
Lecture	36	No Description
Tutorial	12	No Description
Independent learning	150	No Description
Total Workload: 198

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

Indicative Content and Learning Activities

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 adecomposition of the sample space; conditional expectation with respect to a sub s-algebraas 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..

Assessment Breakdown
Continuous Assessment	25%	Examination Weight	75%

Course Work Breakdown
Type	Description	% of total	Assessment Date
In Class Test	n/a	25%	Week 9

Reassessment Requirement
Resit arrangements are explained by the following categories; 1 = A resit is available for all components of the module 2 = No resit is available for 100% continuous assessment module 3 = No resit is available for the continuous assessment component
This module is category 3

Indicative Reading List

Williams, D: 1991, Probability with Martingales, Cambridge University Press,
Lamberton, D., and Lapeyre, B: 1996, Introduction to Stochastic Calculus with FinancialApplications, Chapman and Hall, London,

Other Resources

None

Array

Programme or List of Programmes

BSSA

Study Abroad (DCU Business School)

BSSAO

Study Abroad (DCU Business School)

ECSA

Study Abroad (Engineering & Computing)

ECSAO

Study Abroad (Engineering & Computing)