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## MTHM002 - Methods for Stochastics and Finance (2019)

MODULE TITLE | Methods for Stochastics and Finance | CREDIT VALUE | 15 |
---|---|---|---|

MODULE CODE | MTHM002 | MODULE CONVENER | Prof Andrew Gilbert (Coordinator) |

DURATION: TERM | 1 | 2 | 3 |
---|---|---|---|

DURATION: WEEKS | 11 weeks | 0 | 0 |

Number of Students Taking Module (anticipated) | 58 |
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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.

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.

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.

- 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.

Scheduled Learning & Teaching Activities | 33.00 | Guided Independent Study | 117.00 | Placement / Study Abroad |
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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 |

Form of Assessment | Size of Assessment (e.g. duration/length) | ILOs Assessed | Feedback Method |
---|---|---|---|

Coursework – example sheet 1 | 500 words -10 hours | 1,2,3 | Written/tutorial |

Coursework – example sheet 2 | 500 words -10 hours | 1, 2, 3 | Written/tutorial |

Coursework | 0 | Written Exams | 100 | Practical Exams |
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Form of Assessment | % of Credit | Size of Assessment (e.g. duration/length) | ILOs Assessed | Feedback Method |
---|---|---|---|---|

Written exam – closed book | 100 | 2 hours | 1,2,3 | Written/verbal on request |

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 |

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 50% 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.

information that you are expected to consult. Further guidance will be provided by the Module Convener

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

Reading list for this module:

Type | Author | Title | Edition | Publisher | Year | ISBN | Search |
---|---|---|---|---|---|---|---|

Set | Gerald C.F. & Wheatley P.O. | Applied Numerical Analysis | 7th | Anderson-Wesley | 2004 | 978-8131717400 | [Library] |

Set | Mikosch T. | Elementary stochastic calculus with finance in view | World Scientific | 1998 | 000-9-810-23543-7 | [Library] | |

Set | Martinez W.L. & Martinez A.R. | Computational statistics handbook with MATLAB | Chapman & Hall | 2001 | 000-1-584-88229-8 | [Library] | |

Set | Kharab, A. & Guenther, R.B. | An Introduction To Numerical Methods: A MATLAB Approach | Chapman & Hall | 2012 | 978-1439868997 | [Library] |

CREDIT VALUE | 15 | ECTS VALUE | 7.5 |
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PRE-REQUISITE MODULES | None |
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CO-REQUISITE MODULES | None |

NQF LEVEL (FHEQ) | 7 | AVAILABLE AS DISTANCE LEARNING | No |
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ORIGIN DATE | Tuesday 10 July 2018 | LAST REVISION DATE | Tuesday 10 July 2018 |

KEY WORDS SEARCH | Stochastic; financial mathematics; matrices; dissemination equations; approximation theory. |
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