Malliavin calculus for subordinated Lévy process

Abstract

We develop a chaos expansion for a subordinated Lévy process. This expansion is expressed in terms of Itô’s multiple integral expansion. Considering the jumps occurring due to an underlying process and a subordinator, a mixed chaotic representation is proposed. This representation provides the definition of the Malliavin derivative, which is characterized by increment quotients. Moreover, we introduce a new Clark–Ocone expansion formula for the subordinated Lévy process and provide applications for risk-free hedging in a designed model.