Postgraduate Course: Stochastic Control and Dynamic Asset Allocation (MATH11150)
Course Outline
| School | School of Mathematics |
College | College of Science and Engineering |
| Credit level (Normal year taken) | SCQF Level 11 (Postgraduate) |
Availability | Not available to visiting students |
| SCQF Credits | 10 |
ECTS Credits | 5 |
| Summary | 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, nonlinear PDEs), and the underlying ideas unifying them. |
| Course description |
- 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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Course Delivery Information
|
| Academic year 2019/20, Not available to visiting students (SS1)
|
Quota: None |
| Course Start |
Semester 2 |
Timetable |
Timetable |
| Learning and Teaching activities (Further Info) |
Total Hours:
100
(
Lecture Hours 16,
Seminar/Tutorial Hours 4,
Programme Level Learning and Teaching Hours 2,
Directed Learning and Independent Learning Hours
78 )
|
| Assessment (Further Info) |
Written Exam
100 %,
Coursework
0 %,
Practical Exam
0 %
|
| Additional Information (Assessment) |
Examination 100% |
| Feedback |
Not entered |
| Exam Information |
| Exam Diet |
Paper Name |
Hours & Minutes |
|
| Main Exam Diet S2 (April/May) | Stochastic Control and Dynamic Asset Allocation (MATH11150) | 2:00 | |
Learning Outcomes
On completion of this course, the student will be able to:
- Demonstrate knowledge of controlled Markov chains.
- Demonstrate knowledge of, and a critical understanding of, the theory of optimal stopping in discrete time and continuous time.
- Demonstrate knowledge of, and a critical understanding of, Hamilton-Jacobi-Bellman equations.
- Demonstrate knowledge of, and a critical understanding of, variational inequalities.
- Demonstrate understanding of, and critical assessment of, optimal investment-consumption problems.
|
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. |
Additional Information
| Graduate Attributes and Skills |
Not entered |
| Special Arrangements |
MSc Financial Modelling and Optimization and MSc Computational Mathematical Finance students only. |
| Keywords | SCDAA |
Contacts
| Course organiser | Dr David Siska
Tel: (0131 6)51 9091
Email: |
Course secretary | Miss Gemma Aitchison
Tel: (0131 6)50 9268
Email: |
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