Financial/Actuarial Mathematics Seminar

We establish a novel connection between optimal transport theory and the dynamic version of the Kyle model of informed trading. Our methodology based on the Monge-Kantorovich duality and backward stochastic partial differential equations allows us to obtain the existence of equilibrium in all risk-neutral versions of the model studied in the literature and extend the existence results to novel cases. With risk-averse market makers, we show that liquidity is lower, assets exhibit short-term reversals, and risk premia depends 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. Based on joints work with K. Back, S.Bose, R. Chhaibi, F. Cocquemas, A. Lioui, E. Noh, and L. Vy. Speaker(s): Ibrahim Ekren (Florida State University)