Useful links
Unit of study_
MATH4512: Stochastic Analysis
Capturing random phenomena is a challenging problem in many disciplines from biology, chemistry and physics through engineering to economics and finance. There is a wide spectrum of problems in these fields, which are described using random processes that evolve with time. Hence it is of crucial importance that applied mathematicians are equipped with tools used to analyse and quantify random phenomena. This unit will introduce an important class of stochastic processes, using the theory of martingales. You will study concepts such as the Ito stochastic integral with respect to a continuous martingale and related stochastic differential equations. Special attention will be given to the classical notion of the Brownian motion, which is the most celebrated and widely used example of a continuous martingale. By completing this unit, you will learn how to rigorously describe and tackle the evolution of random phenomena using continuous time stochastic processes. You will also gain a deep knowledge about stochastic integration, which is an indispensable tool to study problems arising, for example, in Financial Mathematics.
| Code | MATH4512 |
|---|---|
| Academic unit | Mathematics and Statistics Academic Operations |
| Credit points | 6 |
|
Prerequisites:
?
|
None |
|---|---|
|
Corequisites:
?
|
None |
| Prohibitions:
?
|
None |
| Assumed knowledge:
?
|
Students should have a sound knowledge of probability theory and stochastic processes from, for example, STAT2X11 and STAT3021 or equivalent |
At the completion of this unit, you should be able to:
- LO1. Demonstrate an understanding of the concepts of continuous time processes, stopping times and martingales.
- LO2. Apply the properties of Brownian motion (such as martingale property, Markov property, behaviour under the equivalent change of measure and predictable representation property).
- LO3. Describe the construction of Ito integral and apply Ito integration correctly in relevant examples.
- LO4. Identify the similarities and differences between strong and weak solutions to SDEs and apply existence and uniqueness results to some specific SDEs.
- LO5. Check the martingale property of stochastic processes using Ito's lemma.
- LO6. Use the Feymann Kac formula to analyse real world problems including arbitrage pricing.
- LO7. Identify, formulate and solve original practical problems that can be addressed using mathematical techniques learnt in this unit and examine the implementations and provide an interpretation of the results.
- LO8. Independently research sources provided by lecturers such as journal articles and working papers and evaluate the real-world plausibility and effectiveness of various approaches and tools.
Unit outlines
Unit outlines will be available 2 weeks before the first day of teaching for the relevant session.
- Semester 2, 2024 [Normal day] - Camperdown/Darlington, Sydney
- Key dates
Key dates through the academic year, including teaching periods, census, payment deadlines and exams.
- Student administration
Enrolment, course planning, fees, graduation, support services, student IT
- Expectations of student conduct
Code of Conduct for Students, Conditions of Enrollment, University Privacy Statement, Academic Integrity
- Academic appeals
Academic appeals process, special consideration, rules and guidelines, advice and support
- Learning and teaching policy
Policy register, policy search
- Financial support
Scholarships, interest free loans, bursaries, money management
- Study resources
Learning Centre, faculty and school programs, Library, online resources
- Health and support
Student Centre, counselling & psychological services, University Health Service, general health and wellbeing
