  A new method for stochastic control based on neural networks and using
randomisation of discrete random variables is proposed and applied to optimal
stopping time problems. The method models directly the policy and does not need
the derivation of a dynamic programming principle nor a backward stochastic
differential equation. Unlike continuous optimization where automatic
differentiation is used directly, we propose a likelihood ratio method for
gradient computation. Numerical tests are done on the pricing of American and
swing options. The proposed algorithm succeeds in pricing high dimensional
American and swing options in a reasonable computation time, which is not
possible with classical algorithms.
