Mathematical Finance Seminar
Ibrahim Ekren (Florida State)

Optimal transport and risk aversion i Kyle's model of informed trading

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 mar- ket makers, liquidity is lower, assets exhibit short-term reversals, and risk premia depend on market maker inventories, which are mean re- verting. 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.