  We establish connections between optimal transport theory and the dynamic
version of the Kyle model, including new characterizations of informed trading
profits via conjugate duality and Monge-Kantorovich duality. We use these
connections to extend the model to multiple assets, general distributions, and
risk-averse market makers. With risk-averse market makers, liquidity is lower,
assets exhibit short-term reversals, and risk premia depend on market maker
inventories, which are mean reverting. We illustrate the model by showing that
implied volatilities predict stock returns when there is informed trading in
stocks and options and market makers are risk averse.
