Course co-ordinator(s): Dr Goncalo Dos Reis (Edinburgh).
Aims:
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.
Summary:
- 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.
Detailed Information
Course Description: Link to Official Course Descriptor.
Pre-requisites: none.
Location: Edinburgh.
Learning Outcomes: Subject Mastery
- 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.
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.
SCQF Level: 11.
Other Information
Help: If you have any problems or questions regarding the course, you are encouraged to contact the course leader.
Canvas: further information and course materials are available on Canvas