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Unit of study_
MATH5551: Stochastics and Finance
2025 unit information
Stochastics examines phenomena in which chance plays a central role. The theory of stochastic phenomena has applications in engineering systems, the physical and life sciences and economics, to give just a few examples. Applications of stochastic processes arise particularly naturally in finance where there are fluctuations in stock prices and practitioners are required to solve different types of optimisation problems in stochastically driven systems. For this reason, it is particularly important that mathematicians in general and especially mathematicians specialising in problems in the financial industry are equipped with tools to analyse and quantify random phenomena. This unit will expose you to critical topics in the theory and application of stochastic processes and analysis in mathematical finance. You will learn how to identify problems that require the application of stochastic theory, how to rigorously describe such problems using appropriate mathematical frameworks and how to tackle and solve the problem once it has been phrased in terms of stochastic theory. Along the way, you will also gain a deep knowledge about diverse topics in finance and the relevance of mathematical analysis in the financial industry.
Unit details and rules
Managing faculty or University school:
Science
| Study level | Postgraduate |
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| Academic unit | Mathematics and Statistics Academic Operations |
| Credit points | 6 |
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Prerequisites:
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None |
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Corequisites:
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None |
| Prohibitions:
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None |
| Assumed knowledge:
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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 familiarity with fundamental concepts in the general theory of stochastic processes.
- LO2. Understand the concept of a backward stochastic differential equation and the proof of the main existence and uniqueness of solutions theorem.
- LO3. Understand the comparison property for solutions to a BSDE and its applications to other stochastic problems.
- LO4. Be capable of analysing optimal stopping problems using a reflected BSDE.
- LO5. Analyse two-person stochastic Dynkin games using a doubly reflected BSDE.
- LO6. Analyse and solve optimal control problems via the Hamilton-Jacobi-Bellman equation.
- LO7. Analyse optimal control problems via the stochastic Pontryagin principle.
- LO8. Analyse stochastic differential games and identify its value process.
- LO9. Analyse and apply the Feynman–Kac formula for solutions to quasi-linear parabolic PDEs.
Unit availability
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| Session | MoA ? | Location | Outline ? |
|---|---|---|---|
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Semester 2 2025
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Normal day | Camperdown/Darlington, Sydney |
Outline unavailable
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Important enrolment information
Additional advice
This unit is only available in odd years.
