Skip to main content
Unit of study_

Optimal Control and Game Theory - MATH5550

Year - 2020

How to maximise gains (or to minimise costs) and how to determine optimal strategies or policies are fundamental questions for engineers, economists, doctors designing a cancer therapy, fund managers or a government agency planning social policies. Several problems in Science (e. g. mechanics, physics, neuroscience or biology) can be also formulated as optimisation problems in random environments. The theory of stochastic optimal control and games is an indispensable tool in many areas of applied mathematics. In the first part of this unit, you will be familiarised with the dynamic programming principle and learn how to show that it provides a unified approach to a large number of seemingly unrelated problems. The second part is devoted to backward stochastic differential equations and their applications to stochastic optimal control and game theory. You will learn how to solve continuous time problems based either on the Wiener process or more general classes of stochastic processes. After completing this unit, you will be able to formulate a diverse suite of problems arising in finance, applied sciences, engineering and medicine as stochastic optimal control problems and solve them using the concepts of the Bellman principle, Hamilton-Jacobi-Bellman equation and backward stochastic differential equations.

Classes
3 x 1 hr lectures and 1 x 1hr tutorial per week for 13 weeks

Assessment
2 x take-home assignments (40%), final exam (60%)

Additional information
This unit is only available in even years.

Assumed knowledge
At least 6 credit points of (2000-level Advanced Mathematics or 3000-level Advanced Mathematics or 4000-level Mathematics units) or equivalent.

Details

Faculty: Science

Semester 2

03 Aug 2020

Department/School: Mathematics and Statistics Academic Operations
Study Mode: Normal (lecture/lab/tutorial) day
Census Date: 31 Aug 2020
Unit of study level: Postgraduate
Credit points: 6.0
EFTSL: 0.125
Available for study abroad and exchange: Yes
Faculty/department permission required? No
Location
Camperdown
More details
Unit of Study coordinator: Oded Yacobi
HECS Band: 2
Courses that offer this unit

Non-award/non-degree study If you wish to undertake one or more units of study (subjects) for your own interest but not towards a degree, you may enrol in single units as a non-award student. Cross-institutional study If you are from another Australian tertiary institution you may be permitted to undertake cross-institutional study in one or more units of study at the University of Sydney.

To help you understand common terms that we use at the University, we offer an online glossary.