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

The existence of an adapted solution to a backward stochastic differential equation which is not adapted to the ltration 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 di erent information about the evolution of the market. The problem is considered in both the classical and the F ollmer-Schweizer hedging case. key-words: backward stochastic di erential equations, pricing of contingent claims, anticipative information AMS subject classi cation: 35K55, 90A09, 93E20 Universitat Konstanz, Fakultat f ur Mathematik und Informatik, D-78457 Konstanz, Germany, supported by The Center of Finance and Econometrics. email: [email protected] Department of Systems Engineering and Engineering Management, The Chinese University of Hong Kong. email: [email protected]. Supported by the RGC Earmarked Grant CUHK 4125/97E and 4054/98E. This research was done while this author was visiting Michael Kohlmann at Konstanz. The support from the DAAD is gratefully acknowledged.