Standard models for financial markets are based on the simplifying assumption that trading orders can be given and executed in continuous time with no friction. This assumption is clearly a strong idealization of the reality. In particular, securities should not be described by a single price but by a bid and ask curve. As a first approximation, one may assume that the bid and ask prices do not depend on the traded quantities which leads to models with proportional transaction costs. These models have attracted a lot of attention these lasts years, mostly because their linear structure allows to develop a nice duality theory as in frictionless models.
