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A new method for stochastic control based on neural networks and usingrandomisation of discrete random variables is proposed and applied to optimalstopping time problems. The method models directly the policy and does not needthe derivation of a dynamic programming principle nor a backward stochasticdifferential equation. Unlike continuous optimization where automaticdifferentiation is used directly, we propose a likelihood ratio method forgradient computation. Numerical tests are done on the pricing of American andswing options. The proposed algorithm succeeds in pricing high dimensionalAmerican and swing options in a reasonable computation time, which is notpossible with classical algorithms.

Deep combinatorial optimisation for optimal stopping time problems : application to swing options pricing