We discuss problems where impact from optimal or equilibrium trading leads to challenging nonlinear systems and fixed point problems. These may arise from
i) Market impact from a significant group of portfolio optimizers in a constrained market with clearing conditions. ii) High frequency trading to a target.
iii) Oligopolies with a small number of influential players, or a continuum of players with aggregate impact.
iv) Optimal execution where trading speed is penalized.
These are addressed with computational and analytical methods, and well-posedness of the problems is crucial in the absence of general theory. Speaker(s): Ronnie Sircar (Princeton University)