Postgraduate Course: Stochastic Control and Dynamic Asset Allocation (MATH11150)
|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
|Summary||The course presents an introduction to control theory and its applications. This is an active area of research, both in pure and applied mathematics. The applications are in engineering, finance and economics. The course focuses on developing methods for solving control problems and offers an opportunity to see the connections between different fields, (controlled dynamical systems, optimization, nonlinear PDEs), and the underlying ideas unifying them.
- 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 and verification theorems
- Pontryagin optimality criteria and backward stochastic differential equations
- Applications in finance and economics: Merton's investment problem, optimal execution problems, optimal production, linear-quadratic control problems
- Algorithms for computationally solving control problems: policy iteration, value iteration, method of successive approximation.
Course Delivery Information
|Academic year 2022/23, Not available to visiting students (SS1)
|Learning and Teaching activities (Further Info)
Lecture Hours 16,
Seminar/Tutorial Hours 4,
Programme Level Learning and Teaching Hours 2,
Directed Learning and Independent Learning Hours
|Assessment (Further Info)
|Additional Information (Assessment)
||Hours & Minutes
|Main Exam Diet S2 (April/May)||Stochastic Control and Dynamic Asset Allocation (MATH11150)||2:00|
On completion of this course, the student will be able to:
- Solve problems involving controlled Markov Chains using the dynamic programming and backward induction.
- Solve problems involving controlled SDEs using the Bellman PDE and be able to justify the use of the Bellman PDE in such problems by reference to relevant proofs.
- Solve problems involving controlled ODEs or SDEs using the Pontryagin optimality principle and be able to justify the use of Pontryagin optimality in such problems by reference to relevant proofs.
- Implement policy iteration / value iteration or method of successive approximation algorithms using an appropriate programming language (e.g. Python) to solve control problems numerically.
|-H. Pham: Continuous-time stochastic control and optimization with financial applications, Series SMAP, Springer 2009. |
-D. Bertsekas: Dynamic Programming and Optimal Control, Vols. I and II,¿Athena Scientific, 1995, (4th Edition Vol. I, 2017, 4th Edition Vol. II, 2012).¿
- A. Cartea, S. Jaimungal, and J. Penalva. Algorithmic and High-Frequency Trading. Cambridge University Press, 2015.
|Graduate Attributes and Skills
||MSc Financial Modelling and Optimization and MSc Computational Mathematical Finance students only.
|Course organiser||Dr David Siska
Tel: (0131 6)51 9091
|Course secretary||Miss Gemma Aitchison
Tel: (0131 6)50 9268