Markowitz portfolio selection is a cornerstone in finance, in academia as well as in the industry. Most academic studies either ignore transaction costs or account for them in a way that is both unrealistic and suboptimal by (i) assuming transaction costs to be constant across stocks and (ii)...

We extend recurrent neural networks to include several flexible timescales for each dimension of their output, which mechanically improves their abilities to account for processes with long memory or highly disparate timescales. We compare the ability of vanilla and extended long short-term...