Bouchard, B., & Jouini, E (2010).
Encyclopedia of quantitaive finance.
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..