An optimal transport problem with backward martingale constraints motivated by insider trading

Abstract

We study a single-period optimal transport problem on ${\mathbb{R}}^2$ with a covariance-type cost function $c(x,y)=(x_1-y_1)(x_2-y_2)$ and a backward martingale constraint. We show that a transport plan $\gamma$ is optimal if and only if there is a maximal monotone set $G$ that supports the $x$-marginal of $\gamma$ and such that $c(x,y)={\min }_{z\in G}c(z,y)$ for every $(x,y)$ in the support of $\gamma$. 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).

46 pages

Cited by in corpus (4)

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