Introducing Optimal Execution Strategies in Limit Order Books with General Shape Functions for after-work quants

Takeaway. Optimal block execution depends on the shape of the book and how fast depth resilience recovers after you take liquidity—not only on a single impact number.

Optimal Execution Strategies in Limit Order Books with General Shape Functions (Aurélien Alfonsi, Antje Fruth, Alexander Schied, 2007) generalises Obizhaeva–Wang-style ideas to arbitrary LOB shapes with explicit discrete-time strategies.

Fit for learners: Generalizes Obizhaeva–Wang to arbitrary LOB shapes with explicit discrete-time optimal block execution under resilience.

This Hub note is a plain-language intro. Not investment advice. Related: Almgren–Chriss, Guéant block-trade pricing.

The problem

Many execution toys assume a flat impact coefficient. Real books have depth that is uneven across prices, and after you sweep a level the book refills only gradually. Ignoring shape and resilience misprices urgency.

The idea / core intuition

• Model the LOB with a shape function: how much size sits at each distance from mid.
• After a block trade, depth recovers with a resilience rule toward a steady shape.
• Optimal policy often looks like carefully timed discrete blocks—not continuous drip only.
• Changing the shape changes how aggressive early vs late child orders should be (in the model).

Read the PDF for theorems and examples. Study only—no live slicing from this note.

Why after-work Python learners care

Shape + resilience is a clean object to code: arrays for depth, a refill step, and a cost function over schedules.

Tiny evening exercise: make a length-10 depth array, "execute" a block that eats the first few levels, then apply a simple refill toward the original shape for 5 steps—plot depth each step.

One-evening reading checklist

1. Paraphrase "shape function" and "resilience."
2. Note discrete-time vs continuous-time framing.
3. Ask how this differs from Almgren–Chriss temporary/permanent impact.
4. Sketch when a more aggressive first block might be optimal in-model.

Download PDF

Download PDF

Landing: arXiv:0708.1756

Important disclaimer

Not investment advice. This Hub note is educational only. The paper is research—not a licence to trade, quote, or execute with real capital.

What this is not

• Not CEF / subsidy framing
• Not Quant or Macro course CTA
• Not a broker / signal-group pitch

Next step

Single course CTA: SoloQuant Academy's Introduction to Python Programming—get comfortable with functions, files, and plots first; then these microstructure PDFs become much less scary.