MATH40690 Stochastic Calculus

Academic Year 2023/2024

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.

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Curricular information is subject to change

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.

Student Effort Hours: 
Student Effort Type Hours
Lectures

30
Tutorial

10
Specified Learning Activities

60
Autonomous Student Learning

100
Total

200
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 Open Book Exam Component Scale Must Pass Component % of Final Grade
Continuous Assessment: Two 50-minute written tests held in class. Throughout the Trimester n/a Standard conversion grade scale 40% No

40
Examination: Final Exam in December 2 hour End of Trimester Exam No Standard conversion grade scale 40% No

60

Carry forward of passed components
No
 
Resit In Terminal Exam
Spring Yes - 2 Hour
Please see Student Jargon Buster for more information about remediation types and timing. 
Feedback Strategy/Strategies

• Group/class feedback, post-assessment

How will my Feedback be Delivered?

Not yet recorded.

Timetabling information is displayed only for guidance purposes, relates to the current Academic Year only and is subject to change.
 
Autumn
      
Lecture Offering 1 Week(s) - Autumn: All Weeks Fri 11:00 - 11:50
Lecture Offering 1 Week(s) - Autumn: All Weeks Mon 11:00 - 12:50
Lecture Offering 1 Week(s) - 1, 2, 4, 5, 6, 7, 8, 9, 10, 11, 12 Wed 11:00 - 11:50
Lecture Offering 1 Week(s) - 3 Wed 11:00 - 11:50
Autumn