Necessary and Sufficient

In an ACM journal a little while back was a reprint of a very interesting academic paper addressing the problem of allocating a large order efficiently across a number of "dark pools" (alternate trading exchanges).

The approach the authors use is an exploration-exploitation loop whereby they treat the "demand" at each dark pool as a (censored) random drawing from an unknown distribution in the exploration phase, using modified Kaplan-Meier maximum likelihood estimators in the process, and then employ a greedy algorithm to exploit the current information.

It's a very clever approach and worth a read. You can find the paper here. I'm sure it hasn't gone unnoticed by Hedge funds, investment banks and prop-trading outfits!