Stochastic Control and Dynamic Asset Allocation (SCDAA), 2019-20

Useful to know

The course lecturer and organiser is David Siska, School of Mathematics, Room 4611.

This is Semester 2 course. The course timetable is here: timetable.

The course details are here: course details.

Partial lecture notes

The lecture notes can be downloaded here (last update 14th February 2020).

Inevitably, there are mistakes in the lecture notes. Please report those to me! I will keep track of who reported how many mistakes and the "winner" will be announced after the exam. If anything is not clear, ask.

Problem sheets

Problem sheet 1 for Week 1 (last update 17th January 2020).
Problem sheet 2 for Week 3 (last update 31st January 2020).
Problem sheet 3 for Week 5 (last update 14th February 2020).
Problem sheet 4 for Week 7 (last update 6th March 2020).

Past exam papers

Download the 2015/16 exam or download the 2015/16 questions and solutions (but note that not all questions may be relevant as course material changed).
Download the 2016/17 exam or download the 2016/17 questions and solutions (but note that not all questions may be relevant as course material changed).
Download the 2017/18 exam or download the 2017/18 questions and solutions (but note that not all questions may be relevant as course material changed).
Download the 2018/19 exam or download the 2018/19 questions and solutions.

Assessment

The course assessment is 100% exam. The exam takes place in May and all exam questions count towards final mark.

Books and other sources

It is recommended that you read / understand / tackle exercises in the relevant parts of:

H. Pham - Continuous-time stochastic control and optimization with financial applications, Springer, 2009 (available for download via the Library - you may need to use a university computer for this).
N. Touzi - Optimal Stochastic Control, Stochastic Target Problems and Backward SDE (online lecture notes, free to download). There is a local copy in case the previous link fails: local copy.

Outline - expected, we'll see how fast we go:

Week 1: Introductory examples.
Week 2: Discrete space time (controlled Markov chains), Bellman princple and equation.
Week 3: Value and policy iteration, Q-learning. Download the Qlearning-example.ipynb Python notebook for the simple example discussed.
Week 4: Controlled SDEs, existence, uniquness, Markov and flow properties.
Week 5: Bellman Principle / DPP for controlled SDEs.
Flexible learning week.
Week 6: Bellman PDE / HJB equation.
Week 7: HJB verification theorem, solving the Merton problem, solving linear-quadratic control problem.
Week 8: BSDEs - examples, existence, uniqueness.
Week 9: Pontryiagin's optimality principle.
Week 10: Solving minimum-variance for given return problem.
Week 11: Revision.