Sophie Laruelle Université Paris-Est Créteil (UPEC) After presenting stochastic approximation algorithms and recalling some results on convergence and weak rate, we will focuse on applications of this theory to optimal execution throughout three examples : optimal split of large volume across liquidity pools, optimal posting price of limit order and both simultaneously. For each example, the model and the algorithm design will be introduced as well as convergence results. Numerical experiments on both simulated and market data will illustrate each framework.