Private information and the use of a so called 'information function'

The literature on private information as a source of trade is probably most well known via the seminal work by Jean Tirole and Paul Milgrom and Nancy Stokey. We consider an arbitrage opportunity to be the result of the existence of such private information. We are interested to propose a model which can accommodate the presence of arbitrage. A major ingredient in our proposed model is the concept of ‘information function’. We discuss in detail some of the characteristics of this function and propose how it can be used, amongst other uses in an arbitrage based option pricing model.