Stochastic Control and Dynamic Asset Allocation (SCDAA), 2022-23

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.

The course Learn page is here: course Learn page.

The Piazza discussion forum is here: Piazza forum.

The office hours are Tueasdays 4:15pm-5:00pm in JCMB 4611 every week during the term.

Partial lecture notes

The lecture notes can be downloaded here (last update 21st March 2023). The lecture notes cover material that will not be taught this year and at the same time there is material which will be taught this year that's not in the notes.

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 notes typos scoreboard

Empty for the moment; find mistakes in the lecture notes and your name will appear. The student who reports the most by the end of the exams will be the winner.

Plan for 2022-23

Week 1: Introductory examples.
Week 2: Wrap up examples, structure of control problem.
Week 3: Bellman Principle, PDE and an example.
Week 4: Pontryagin optimality and an example.
Week 5: Proof of Bellman Principle, PDE, verification. Coursework handed out.
Week 6: Proof of Bellman Principle, PDE, verification.
Week 7: Poisson process, Ito formula for jump diffusions.
Week 8: Controlled jump intensity, Bellman principle and PDE for jump diffusion.
Week 9: Application: optimal liquidation with limit orders.
Week 10: Application: optimal spread for limit orders in market making.
Week 11: Anything we've not had time for + work on coursework and revision. Coursework hand in date - Friday Week 11.

Problem sheets

These will be added here before each workshop.

Problem sheet 1 for Week 1 (last update January 2023).
Problem sheet 2 for Week 3 (last update January 2023).
Problem sheet 3 for Week 5 (last update February 2023).
Problem sheet 4 for Week 7 (last update March 2023).
Problem sheet 5 for Week 9 (last update March 2023).

Past exam papers

Note that not all questions may be relevant as course materials changed.

Assessment

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

The continuous assesment will constitute one piece of coursework which will be made available at the end of Week 5. Coursework deadline: Friday 7th April 2023 at 12:01pm (i.e. one minute after noon Friday of Week 11). You can find the coursework tasks on the course Learn page under "Assement".

The exam takes place in the May/June exam period 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).
A. Cartea and S. Jaimungal and J. Penalva - Algorithmic and high-frequency trading, Cambridge University Press, 2015.
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 videos created during Covid

Feel free to ignore the videos. They contain material we will not be covering in 2022-23 and there is material we will be covering but that's not in the videos. They are available in case you find them useful - and the descriptions should tell you enough to get you started.

There are also the lecture recordings from the set of lectures taught in 2022-23 available via Learn. Depending on the room these may or may not be useful. You can make them more useful by reminding your lecturer to wear the microphone and switch the camera to the relevant board (if appropriate). It is strongly recommended that you do not rely on those and come to lectures.

Try watching at 1.5x or 2x speed and pausing as you need.

Set 1: Introductory examples.
Set 2: Discrete space time (controlled Markov chains), Bellman princple and equation.
Set 3: Value and policy iteration, Q-learning.
Set 4: Controlled SDEs (existence, uniquness, Markov and flow properties). Continuous space time control problems.
Set 5: Bellman Principle / DPP for controlled SDEs.
Set 6: Bellman PDE / HJB equation. HJB verification theorem, solving the Merton problem, solving linear-quadratic control problem.
Set 7: Derivation of Pontryagin optimality (necessary condition), solving linear BSDEs in 1D.
Set 8: Existence and uniqueness of solutions to BSDE under Lipschitz assumption, Pontryagin optimality (sufficient condition) and example: solving LQ problem using Pontryagin.

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