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.
Mots clés : Optimal stopping, American option, Swing option, Combinatorial optimisation, Neural network, Artificial intelligence.
@article{MSIA_2022__11_1_243_0,
author = {Deschatre, Thomas and Mikael, Joseph},
title = {Deep combinatorial optimisation for optimal stopping time problems: application to swing options pricing.},
journal = {MathematicS In Action},
pages = {243--258},
publisher = {Soci\'et\'e de Math\'ematiques Appliqu\'ees et Industrielles},
volume = {11},
number = {1},
year = {2022},
doi = {10.5802/msia.26},
language = {en},
url = {http://www.numdam.org/articles/10.5802/msia.26/}
}
TY - JOUR AU - Deschatre, Thomas AU - Mikael, Joseph TI - Deep combinatorial optimisation for optimal stopping time problems: application to swing options pricing. JO - MathematicS In Action PY - 2022 SP - 243 EP - 258 VL - 11 IS - 1 PB - Société de Mathématiques Appliquées et Industrielles UR - http://www.numdam.org/articles/10.5802/msia.26/ DO - 10.5802/msia.26 LA - en ID - MSIA_2022__11_1_243_0 ER -
%0 Journal Article %A Deschatre, Thomas %A Mikael, Joseph %T Deep combinatorial optimisation for optimal stopping time problems: application to swing options pricing. %J MathematicS In Action %D 2022 %P 243-258 %V 11 %N 1 %I Société de Mathématiques Appliquées et Industrielles %U http://www.numdam.org/articles/10.5802/msia.26/ %R 10.5802/msia.26 %G en %F MSIA_2022__11_1_243_0
Deschatre, Thomas; Mikael, Joseph. Deep combinatorial optimisation for optimal stopping time problems: application to swing options pricing.. MathematicS In Action, Tome 11 (2022) no. 1, pp. 243-258. doi : 10.5802/msia.26. http://www.numdam.org/articles/10.5802/msia.26/
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