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.  Numerical tests are done on the pricing of American and swing options. An extension to impulse control problems is described and applied to options hedging under fixed transaction costs. The proposed algorithms seem to be competitive with the best existing algorithms both in terms of precision and in terms of computation time .
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 .
A
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.
R
An extension to impulse control problems is described and applied to options hedging under fixed transaction costs. The proposed algorithms seem to be competitive with the best existing algorithms both in terms of precision and in terms of computation time
The proposed algorithm succeeds in pricing high dimensional American and swing options in a reasonable computation time, which is not possible with classical algorithms