Malliavin calculus for subordinated Lévy process

Hi Jun Choe, Ji Min Lee, Jung Kyung Lee

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)

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.

Original languageEnglish
Pages (from-to)392-401
Number of pages10
JournalChaos, Solitons and Fractals
Volume116
DOIs
Publication statusPublished - 2018 Nov

Bibliographical note

Funding Information:
We thank an anonymous referee for his/her helpful comments, which improved the clarity of this paper. The authors are supported by NRF under grant 2015R1A5A1009350.

Funding Information:
We thank an anonymous referee for his/her helpful comments, which improved the clarity of this paper. The authors are supported by NRF under grant 2015R1A5A1009350 .

Publisher Copyright:
© 2018 Elsevier Ltd

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematics(all)
  • Physics and Astronomy(all)
  • Applied Mathematics

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