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Deep learning for efficient frontier calculation in finance

We propose deep neural network algorithms to calculate efficient frontier in some Mean-Variance and Mean-CVaR portfolio optimization problems. We show that we are able to deal with such problems when both the dimension of the state and the dimension of the control are high. Adding some additional constraints, we compare different formulations and show that a new projected feedforward network is able to deal with some global constraints on the weights of the portfolio while outperforming classical penalization methods. All developed formulations are compared in between. Depending on the problem and its dimension, some formulations may be preferred.