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In this paper we explore the fundamentals of the Martingale RepresentationTheorem (MRT) and a closely related result, the Clark-Ocone formula. We alsoinvestigate how far these theorems can be taken, notably beyond the regularSobolev spaces, through changes of measures and enlargement of filtrations. Welook at Brownian motion (B.M.) driven continuous martingales as well as Jumpand Levy process-driven martingales.

The Martingale Representation Theorem and Clark-Ocone formula