Postgraduate Course: Stochastic Control and Optimization (MATH11133)
Course Outline
| School | School of Mathematics |
College | College of Science and Engineering |
| Course type | Standard |
Availability | Not available to visiting students |
| Credit level (Normal year taken) | SCQF Level 11 (Postgraduate) |
Credits | 10 |
| Home subject area | Mathematics |
Other subject area | None |
| Course website |
None |
Taught in Gaelic? | No |
| Course description | The course presents an introduction to control theory, to a very active area of research, both in pure and applied mathematics. The aim is to learn the basics of the mathematical theory, and to understand some real-world applications, primarily in finance and economics. It offers an opportunity to see the connections between different fields, (controlled dynamical systems, optimization, onlinear PDEs), and the underlying ideas unifying them. |
Entry Requirements (not applicable to Visiting Students)
| Pre-requisites |
|
Co-requisites | |
| Prohibited Combinations | |
Other requirements | For admission to this course, a good understanding of probability at undergraduate level is required. If in doubt, please consult with the Course Organiser. |
| Additional Costs | None |
Course Delivery Information
| Not being delivered |
Summary of Intended Learning Outcomes
- Knowledge of controlled Markov chains.
- Knowledge of, and a critical understanding of, the theory of optimal stopping in discrete time and continuous time.
- Knowledge of, and a critical understanding of, Hamilton-Jacobi-Bellman equations.
- Knowledge of, and a critical understanding of, variational inequalities.
- Understanding of, and critical assessment of, optimal investment-consumption problems. |
Assessment Information
| Examination 100% |
Special Arrangements
| MSc Financial Modelling and Optimization and MSc Mathematics students only. |
Additional Information
| Academic description |
Not entered |
| Syllabus |
- Discrete time case: Controlled Markov chains, backward induction,
optimal stopping in discrete time.
- Continuous time case: Controlled ODEs, Controlled diffusion processes, Bellman principle, Hamilton-Jacobi-Bellman equations, optimal stopping in continuous time, variational inequalities, Calculating American options in the Black Scholes model, Optimal investment-consumption problems.
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| Transferable skills |
Not entered |
| Reading list |
- H. Pham: Continuous-time stochastic control and optimization with financial applications, Series SMAP, Springer 2009.
- H. M. Soner: Stochastic Optimal Control in Finance, Edizioni della
Normale, 2007.
|
| Study Abroad |
Not entered |
| Study Pattern |
Not entered |
| Keywords | SCO |
Contacts
| Course organiser | Dr Sotirios Sabanis
Tel: (0131 6)50 5084
Email: S.Sabanis@ed.ac.uk |
Course secretary | Mrs Julie Hands
Tel: (0131 6)50 4885
Email: Julie.Hands@ed.ac.uk |
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