Bruno Dupire

Title: Functional Expansions and Signatures

Abstract: This talk recaps old results and establishes new ones in the field of expansion and approximation of functionals, with application to path dependent options. In the static case (functionals of paths of fixed length), we review the Volterra and Wiener series and obtain a new expansion by iteration of the pathwise functional Stratonovich formula. In the dynamic case (functionals of paths of varying length), we obtain a pathwise functional Taylor expansion. Finally we establish links between the various expansions.