We consider the problem of optimizing the expected logarithmic utility of the value of a portfolio in a binomial model with proportional transaction costs with a long time horizon. By duality methods, we can find expressions for the boundaries of the no-trade-region and the asymptotic optimal...

Every submartingale S of class D has a unique Doob–Meyer decomposition S=M+A, where M is a martingale and A is a predictable increasing process starting at 0.