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Choe, Hi Jun; Lee, Ji Min; Lee, Jung-Kyung

Malliavin calculus for subordinated Lévy process. (English) Zbl 1442.60061

Chaos Solitons Fractals 116, 392-401 (2018).
Summary: 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.

MSC:

60H07 Stochastic calculus of variations and the Malliavin calculus
60G51 Processes with independent increments; Lévy processes
91G10 Portfolio theory

Keywords:

subordination; Lévy process; Clark-Ocone formula; chaos expansion; Malliavin derivative; risk-free hedging
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