The Informed and Uniformed Agent's Price of a Contingent Claim

Abstract

The existence of an adapted solution to a backward stochastic differential equation which is not adapted to the filtration of the underlying Brownian motion is proved. This result is applied to the pricing of contingent claims. It allows to compare the prices of agents who have different information about the evolution of the market. The problem is considered in both the classical and the Föllmer-Schweizer hedging case.