AN OPTIMAL TRANSPORT PROBLEM WITH BACKWARD MARTINGALE CONSTRAINTS MOTIVATED BY INSIDER TRADING
成果类型：
Article
署名作者：
Kramkov, Dmitry; Xu, Yan
署名单位：
Carnegie Mellon University
刊物名称：
ANNALS OF APPLIED PROBABILITY
ISSN/ISSBN：
1050-5164
DOI：
10.1214/21-AAP1678
发表日期：
2022
页码：
294-326
关键词：
摘要：
We study a single-period optimal transport problem on 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 is an element of G) c(z,y) for every (x,y) is an element of supp 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 (Rev. Econ. Stud. 61 (1994) 131-152).