A Girsanov Type Theorem Under G-Framework

Abstract

This article establishes a Girsanov type theorem under the G-Framework of Peng [15 Peng , S. 2006 . G-expectation, G-Brownian motion and related calculus of Ito's type. Available at: http://abelsymposium.no/symp2005/preprints/peng.pdf [Google Scholar]]. Our result generalizes the classical Girsanov theorem for Brownian motion [10 Girsanov , I.V. 1960 . On transforming a certain class of stochastic processes by absolutely continuous substitution of measures . Theory Probability and Its Applications 5 : 285 – 301 .[Crossref] , [Google Scholar]]. As an application, we price the European call option when the underlying asset's price follows the Geometric G-Brownian motion.