Methods for Stochastics and Finance - 2023 entry

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.
 

*Please refer to reassessment notes for details on deferral vs. Referral reassessment

Deferrals: Reassessment will be by coursework and/or written exam in the deferred element only. For deferred candidates, the module mark will be uncapped.

Referrals: Reassessment will be by a single written exam worth 100% of the module only. As it is a referral, the mark will be capped at 50%. 

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

Reading list for this module: