The Mathematics of the Martingale Approach

Abstract This chapter presents the two main workhorses of the martingale approach to arbitrage theory: the Martingale Representation Theorem and the Girsanov Theorem. The Martingale Representation Theorem shows that in a Wiener world, every martingale can be written as a stochastic integral w.r.t, the underlying Wiener process. The Girsanov Theorem gives complete control of all absolutely continuous measure transformations in a Wiener world. Practice exercises are included.