  Evolutions of the trading landscape lead to the capability to exchange the
same financial instrument on different venues. Because of liquidity issues, the
trading firms split large orders across several trading destinations to
optimize their execution. To solve this problem we devised two stochastic
recursive learning procedures which adjust the proportions of the order to be
sent to the different venues, one based on an optimization principle, the other
on some reinforcement ideas. Both procedures are investigated from a
theoretical point of view: we prove a.s. convergence of the optimization
algorithm under some light ergodic (or "averaging") assumption on the input
data process. No Markov property is needed. When the inputs are i.i.d. we show
that the convergence rate is ruled by a Central Limit Theorem. Finally, the
mutual performances of both algorithms are compared on simulated and real data
with respect to an "oracle" strategy devised by an "insider" who knows a priori
the executed quantities by every venues.
