Any pointers to smart order splitting algo? Lets say you are executing one share (I am making it simple to discuss), you goal is to get the best possible price but you have to complete executing this one share within a time window... how do you do it? Of course, you should be conservative, and keep a limit order passively waiting for it to be hit... It's not only about how much chance you will get it hit, but also about the question of to wait or not to wait... ------------------------------------------ Moreover, now if you want to execute N shares, how do you do that optimally? I know people talking about TWAP, VWAP, etc. But suppose according to TWAP or VWAP, you come down to the sub-interval level and you have to execute 5 shares within 3 seconds... What's the best way to do those 5 shares in 3 seconds? I mean, even under the TWAP or VWAP framework, you still have to get the best execution result for micro-number of shares... what's the best way to do that? Thank you!
If you know nothing about the future, then execute now. Otherwise, you know whether you should execute your 1 share at the current bid/offer or wait. These are execution benchmarks... ...and people build algorithms that try to replicate or beat the benchmark. Of the two you mentioned, only TWAP could generate the scenario you present, where you need to execute n shares within x seconds. In which case, answer is same as answer to first question you asked (knowing something about future vs. knowing nothing). In the case of VWAP, repeatedly calculate VWAP for security you're transacting. Hit bid or offer when it is <= VWAP price.
There are a few good books on how to meet these benchmarks (twap, vwap, volume participation and so on). It appears the OP is looking for some sort of shortterm predictive algorithm. Doubting there is useful literature about that.