Advances in Mathematical Economics avec W. Schachermayer et N. Touzi, 49-71, 2006.
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..
Jouini, E. (1997).
Wolfgang Runggaldier (Ed.), Financial Mathematics
The theory of asset pricing, which takes its roots in the Arrow-Debreu model, the Black and Scholes formula, has been famalized in a framework by Harrison and Kreps (1979), harrison and Pliska (1979) and Kreps (1981). In these models, securities markets are assumed to be frictionless. The main result is that a price process is arbitrage free (or, equivalently, compatible with some equilibrium) if and only if it is, when appropriately renormalized, a martingale for some equivalent probability measure. The theory of pricing by arbitrage floows from there. Contingent claims can be priced by taking their expected value with respect to an equivalent marti…
Jouini, E., & Kallal, H. , (1992).
Arbitraje en mercados de valores con fricciones .
Cuadernos economicos de ICE.