Stochastic Control and Dynamic Asset Allocation (SCDAA), 2020-21

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.  You will find joining information on Learn "Zoom Links" on the left.

The course details are here: course details.

The course Learn page is here: course Learn page.

Partial lecture notes

The lecture notes can be downloaded here (last update January 2021).

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.

Lecture videos

More recorded material will be added as the Semester progresses. You should try to keep up weekly so that you can effectively participate in the Workshops and also so that you are able to complete the continuous assesment.

Tips: as you watch, make notes as you would for a normal lecture. Keep a list of questions you'd like to ask during the interactive sessions. Try watching at 1.5x or 2x speed and pausing as you need.

• Week 1: Introductory examples.
• Week 2: Discrete space time (controlled Markov chains), Bellman princple and equation.
• Week 3: Value and policy iteration, Q-learning.
• Week 4: Controlled SDEs (existence, uniquness, Markov and flow properties). Continuous space time control problems.
• Week 5: Bellman Principle / DPP for controlled SDEs. Coursework question handed out.
• Flexible learning week.
• Week 6: Bellman PDE / HJB equation. HJB verification theorem, solving the Merton problem, solving linear-quadratic control problem.

Plan for the remaining weeks - we'll see how it will look once recorded:

• Week 7: Derivation of Pontryagin optimality (necessary condition), solving linear BSDEs in 1D.
• Week 8: Existence and uniqueness of solutions to BSDE under Lipschitz assumption, Pontryagin optimality (sufficient condition) and example: solving LQ problem using Pontryagin.
• Week 9 (no videos): Focus on coursework and course review.
• Week 10 (no videos): Focus on coursework and course review.
• Week 11 (no videos): Focus on coursework and course review. Coursework deadline: Monday 5th April 2021 at 12:01pm (i.e. one minute after noon Monday after the end of Week 11).

Problem sheets

• Problem sheet 1 for Week 1 (last update January 2021).
• Problem sheet 2 for Week 3 (last update January 2021).
• Problem sheet 3 for Week 5 (last update January 2021).
• Problem sheet 4 for Week 7 (last update 22nd February 2020).
• Problem sheet 5 for Week 9 (last update 15th March 2020).

Past exam papers

• Download the 2019/20 exam or download the 2019/20 questions and solutions.
• Download the 2018/19 exam or download the 2018/19 questions and solutions.
• 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).

Assessment

The course assessment is 20% continuous assesment and 80% exam.

The continuous assesment will constitute one piece of coursework which can be downloaded here. UPDATE: Coursework deadline: Friday 9th April 2021 at 12:01pm (i.e. one minute after noon Friday of "Week 12").

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.

Lecture notes typos scoreboard:

That's all this page has to say at the moment.