abstract: We study a single-period optimal transport problem with a cost function of given by a general bilinear form and a backward martingale constraint. We show that the role of Kantorovich potentials is played by Fitzpatrick functions. Our study is motivated by a variant of the classical Kyle model of insider trading from Rocher and Vila (1994). The presentation is based on paper with Yan Xu (AAP, 2022) and an ongoing project with Mihai Sirbu.