# Mathematics

## ECMM702 - Methods for Stochastics and Finance (2015)

MODULE TITLE CREDIT VALUE Methods for Stochastics and Finance 15 ECMM702 Dr Ana Rodrigues (Coordinator)
DURATION: TERM 1 2 3
DURATION: WEEKS 11 weeks 0 0
 Number of Students Taking Module (anticipated) 38
DESCRIPTION - summary of the module content

The module explores a diverse range of mathematical topics, emphasising their applications to financial modelling. The topics covered will range from matrix algebra to differential systems and stochastic calculus. This module will play an important role in underpinning the mathematical and computational methods needed for the subsequent modules in the financial mathematics MSc programme.

UG Students: Pre-requisite modules: ECM1701, ECM1707 and ECM2702

AIMS - intentions of the module

The module aims to engender an understanding of the mathematics useful for the theory of financial modelling and financial derivatives. It will also develop the students' mathematical ability and reasoning skills.

INTENDED LEARNING OUTCOMES (ILOs) (see assessment section below for how ILOs will be assessed)

On successful completion of this module, you should be able to:

Module Specific Skills and Knowledge:
1 demonstrate a competence in a broad range of methods for tackling mathematical problems, including solving differential equations, finding series and transforms, linear algebra methods, methods in advanced probability and stochastic calculus.
Discipline Specific Skills and Knowledge:
2 identify the appropriate mathematical tools required to tackle complex mathematical problems.
Personal and Key Transferable/ Employment Skills and  Knowledge:
3 present and communicate your ideas in a mature and methodical manner.

SYLLABUS PLAN - summary of the structure and academic content of the module

- matrix algebra: special matrices;

- systems of equations;

- matrix inversion;

- factorisation: e.g. LU factorization and Cholesky factorization.

- eigenvectors/eigenvalues;

- ortogonal matrices and diagonalisation;

- ODEs and PDEs: finite differences;

- single-step methods;

- initial value and boundary value problems;

- eigenvalue problems;

- Laplace's equation and the diffusion equation;

-  techniques in probability: sets, measure, random variables, distributions.

-  probability models and introduction to stochastic processes

- ;Markov chains and random walks

- almost sure convergence and Borel Cantelli Lemmas

- Stochastic calculus: introduction to Ito calculus and stochastic differential equations;

- simulation and numerical solution of stochastic differential equations.

LEARNING AND TEACHING
LEARNING ACTIVITIES AND TEACHING METHODS (given in hours of study time)
 Scheduled Learning & Teaching Activities Guided Independent Study 33 117
DETAILS OF LEARNING ACTIVITIES AND TEACHING METHODS
 Category Hours of study time Description Scheduled learning and teaching activities 22 Lectures Scheduled learning and teaching activities 11 Workshops Guided independent study 117 Guided independent study

ASSESSMENT
FORMATIVE ASSESSMENT - for feedback and development purposes; does not count towards module grade
Form of Assessment Size of Assessment (e.g. duration/length) ILOs Assessed Feedback Method
Not applicable

SUMMATIVE ASSESSMENT (% of credit)
 Coursework Written Exams 20 80
DETAILS OF SUMMATIVE ASSESSMENT
Form of Assessment % of Credit Size of Assessment (e.g. duration/length) ILOs Assessed Feedback Method
Written exam – closed book 80 2 hours 1,2 In accordance with CEMPS policy
Coursework – example sheet 1 10 500 words -10 hours 1,2,3 Written/tutorial
Coursework – example sheet 2 10 500 words -10 hours 1, 2, 3 Written/tutorial

DETAILS OF RE-ASSESSMENT (where required by referral or deferral)
Original Form of Assessment Form of Re-assessment ILOs Re-assessed Time Scale for Re-reassessment
All above Written exam (100%) All August Ref/Def period

RE-ASSESSMENT NOTES

If a module is normally assessed entirely by coursework, all referred/deferred assessments will normally be by assignment.

If a module is normally assessed by examination or examination plus coursework, referred and deferred assessment will normally be by examination. For referrals, only the examination will count, a mark of 40% being awarded if the examination is passed. For deferrals, candidates will be awarded the higher of the deferred examination mark or the deferred examination mark combined with the original coursework mark.

RESOURCES
INDICATIVE LEARNING RESOURCES - The following list is offered as an indication of the type & level of
information that you are expected to consult. Further guidance will be provided by the Module Convener

ELE: http://vle.exeter.ac.uk