Dmitry Kramkov, Carnegie Mellon University

An Optimal Transport Problem With Backward Martingale Constraints Motivated By Insider Trading
Date
Oct 8, 2019, 4:30 pm5:30 pm
Location
101 - Sherrerd Hall
Event Description

We study a single-period optimal transport problem on R2 with a covariance-type cost function c(x,y)=(x1−y1)(x2−y2) and a backward martingale constraint. We show that a transport plan γγ is optimal if and only if there is a maximal monotone set G that supports the x-marginal of γ and such that c(x,y)=minz∈Gc(z,y) for every (x,y)∈γ. We obtain sharp regularity conditions for the uniqueness of an optimal plan and for its representation in terms of a map. Our study is motivated by a variant of the classical Kyle model of insider trading from Rochet and Vila (1994).

The presentation is based on a joint work with Yan Xu.