I am currently reading a book (Algorithmic and High-Frequency Trading by Cartea, Jaimungal and Penalva) which discusses how to optimise order execution using Stochastic Optimal Control.
Although I have a masters engineering degree from a very reputable university, most of our mathematics was discrete. I am struggling understanding the implementation (I understand the high-level trading concepts) because they are illustrated through mathematical proofs.
For example, one equation describes how to schedule selling a large order by time T, whilst minimising market impact. If you sell a large order in one go, you will cause the price to drop, losing you money. Therefore how do you sell the entire order, without moving the market against you. The seller should spread the transaction over time (selling in multiple, smaller orders).
If v_t is the rate of sending orders at time t we need to solve:
where:
(the paper continues extending the example to account for other factors)
How do I read this?! Are there any fully-worked out examples online, even if they're not trading-related but comparable scenarios?
I have no idea if this really is as complicated as the formulae suggests or its simply the formal representation making it seem more difficult.
If there are any books/papers which would help improve my knowledge in this area, please do recommend.