Explore UCD

UCD Home >

MATH40690

Academic Year 2024/2025

Stochastic Calculus (MATH40690)

Subject:
Mathematics
College:
Science
School:
Mathematics & Statistics
Level:
4 (Masters)
Credits:
10
Module Coordinator:
Assoc Professor Marius Ghergu
Trimester:
Autumn
Mode of Delivery:
Blended
Internship Module:
No
How will I be graded?
Letter grades

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.

About this Module

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

36

Specified Learning Activities

66

Autonomous Student Learning

100

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 Must Pass Component % of Final Grade In Module Component Repeat Offered
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

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 Mon 11:00 - 12:50
Autumn Lecture Offering 1 Week(s) - Autumn: Weeks 2-12 Wed 11:00 - 11:50