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This module is a introduction to stochastic calculus. It begins with fundamental concepts in probability theory, stochastic processes, Brownian motion and martingales, leads on to stochastic integrals, chiefly Itô integrals and their properties, and Itô’s formulae, and finishes with a treatment of stochastic differential equations and a few applications in finance. The existence and properties of Brownian motion, Itô integrals and formulae will be addressed heuristically.
The following topics will be covered.
1. Preliminaries - review of fundamental concepts, stochastic processes, Brownian motion, conditional expectation and martingales.
2. Stochastic Integrals - Riemann integrals and variants, Itô integrals and Itô formulae.
3. Stochastic Differential Equations - review of deterministic ODEs, Itô SDEs and general linear SDEs.
Full lecture notes and full solutions to tutorials will be made available on Brightspace.
The following topics will be covered.
1. Preliminaries - review of fundamental concepts, stochastic processes, Brownian motion, conditional expectation and martingales.
2. Stochastic Integrals - Riemann integrals and variants, Itô integrals and Itô formulae.
3. Stochastic Differential Equations - review of deterministic ODEs, Itô SDEs and general linear SDEs.
Full lecture notes and full solutions to tutorials will be made available on Brightspace.
About this Module
Student Effort Hours:
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Requirements, Exclusions and Recommendations
Not applicable to this module.
Module Requisites and Incompatibles
Not applicable to this module.
Assessment Strategy
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Carry forward of passed components
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