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We develop policy gradients methods for stochastic control with exit time ina model-free setting. We propose two types of algorithms for learning eitherdirectly the optimal policy or by learning alternately the value function(critic) and the optimal control (actor). The use of randomized policies iscrucial for overcoming notably the issue related to the exit time in thegradient computation. We demonstrate the effectiveness of our approach byimplementing our numerical schemes in the application to the problem of sharerepurchase pricing. Our results show that the proposed policy gradient methodsoutperform PDE or other neural networks techniques in a model-based setting.Furthermore, our algorithms are flexible enough to incorporate realistic marketconditions like e.g. price impact or transaction costs.

Policy gradient learning methods for stochastic control with exit time and applications to share repurchase pricing