Considering that a trader or a trading algorithm interacting with markets
during continuous auctions can be modeled by an iterating procedure adjusting
the price at which he posts orders at a given rhythm, this paper proposes a
procedure minimizing his costs. We prove the a.s. convergence of the algorithm
under assumptions on the cost function and give some practical criteria on
model parameters to ensure that the conditions to use the algorithm are
fulfilled (using notably the co-monotony principle). We illustrate our results
with numerical experiments on both simulated data and using a financial market
dataset
