Before revision: Motivated by the financial problem of building financial portfolios which outperform the market,Pal and Wong considered optimal transport on the probability simplex \triangle^n where the cost function is induced by the free energy. We study the regularity of this problemand find that the associated MTW tensor is non-negative definite and in fact constant on \triangle^n \times \triangle^n. We further find^n equipped with probability measures \mu and \nu, respectively.
After revision: Let X and Y be domains of \mathbb{R^n equipped with probability measures \mu and \nu, respectively.