Learning Outcomes:
On successful completion of this module, the student is expected to be able to understand the definitions, theorems and examples covered in all of the topics listed above, and carry out associated computations.
Curricular information is subject to change.
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:
| Student Effort Type | Hours |
|---|---|
| Specified Learning Activities | 66 |
| Autonomous Student Learning | 100 |
| Lectures | 36 |
| Total | 202 |
Approaches to Teaching and Learning:
Lectures, tutorials, enquiry and problem-based learning.Requirements, Exclusions and Recommendations
Not applicable to this module.
Module Requisites and Incompatibles
Pre-requisite:MATH10040 - Numbers & Functions, MATH10320 - Mathematical Analysis, MATH10350 - Calculus (MPS), STAT20110 - Introduction to Probability
Incompatibles:
MATH40780 - Stochastic Calculus (online)
Additional Information:
MATH30360/MATH40430 is strongly recommended and must be taken concurrently if this has not been taken before. Either ACM30220 or ACM30080 are strongly recommended. ACM30080 must be taken concurrently if neither module has been taken before.
Assessment Strategy
| Description | Timing | Component Scale | % of Final Grade | ||
|---|---|---|---|---|---|
| Exam (In-person): Final Exam will be two hours long and will take place at the end of the semester. | Week 14, Week 15 | Standard conversion grade scale 40% | No | 60 |
No |
| Assignment(Including Essay): Two written assignments during the semester. | Week 5, Week 10 | Standard conversion grade scale 40% | No | 40 |
No |
| Resit In | Terminal Exam |
|---|---|
| Spring | Yes - 2 Hour |
Feedback Strategy/Strategies
• Group/class feedback, post-assessment
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