We will provide explicit solutions to certain systems linear stochastic Fredholm equations. We will then show the versatility of these equations for solving various optimal trading problems with transient impact including: (i) cross-impact (multiple assets), (ii) constraints on the inventory and trading speeds, and (iii) N-player game and mean-field interactions (multiple traders).

Based on joint works with Nathan De Carvalho, Eyal Neuman, Huyˆen Pham, Sturmius Tuschmann, and Moritz Voss.