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DEGREE REGULATIONS & PROGRAMMES OF STUDY 2019/2020

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DRPS : Course Catalogue : School of Mathematics : Mathematics

Postgraduate Course: Stochastic Control and Dynamic Asset Allocation (MATH11150)

Course Outline
SchoolSchool of Mathematics CollegeCollege of Science and Engineering
Credit level (Normal year taken)SCQF Level 11 (Postgraduate) AvailabilityNot available to visiting students
SCQF Credits10 ECTS Credits5
SummaryThe 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.
Entry Requirements (not applicable to Visiting Students)
Pre-requisites Students MUST have passed: Probability, Measure & Finance (MATH10024) OR Stochastic Analysis in Finance (MATH11154)
Co-requisites
Prohibited Combinations Other requirements PGT students should have taken Stochastic Analysis in Finance (MATH11154). UG students should have taken Probability, Measure and Finance (MATH10024)
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:
  1. Demonstrate knowledge of controlled Markov chains.
  2. Demonstrate knowledge of, and a critical understanding of, the theory of optimal stopping in discrete time and continuous time.
  3. Demonstrate knowledge of, and a critical understanding of, Hamilton-Jacobi-Bellman equations.
  4. Demonstrate knowledge of, and a critical understanding of, variational inequalities.
  5. 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.
KeywordsSCDAA
Contacts
Course organiserDr David Siska
Tel: (0131 6)51 9091
Email: D.Siska@ed.ac.uk
Course secretaryMiss Gemma Aitchison
Tel: (0131 6)50 9268
Email: Gemma.Aitchison@ed.ac.uk
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