Optimal Allocation Strategies for the Dark Pool Problem

We study the problem of allocating stocks to dark pools. We propose and analyze an optimal approach for allocations, if continuous-valued allocations are allowed. We also propose a modification for the case when only integer-valued allocations are possible. We extend the previous work on this problem (Ganchev et al., 2009) to adversarial scenarios, while also improving over their results in the iid setup. The resulting algorithms are efficient, and perform well in simulations under stochastic and adversarial inputs.