Malliavin calculus for subordinated Lévy process

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

Chaos, Solitons & Fractals, 2018, vol. 116, issue C, 392-401

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.

Keywords: Subordination; Lévy process; Clark–Ocone formula; Chaos expansion; Malliavin derivative; Risk-free hedging; Primary 60h07; Secondary 60g51. (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:116:y:2018:i:c:p:392-401

DOI: 10.1016/j.chaos.2018.09.027

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