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

We study a single-period optimal transport problem on R2 with covariance-type cost function c(x,y)=(x1−y1)(x2−y2) and backward martingale constraint. show that plan γ is if only there maximal monotone set G supports the x-marginal of such c(x,y)=minz∈Gc(z,y) for every (x,y)∈suppγ. obtain sharp regularity conditions uniqueness an its representation in terms map. Our motivated by variant classical Kyle model insider trading from (Rev. Econ. Stud. 61 (1994) 131–152).