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A simple proof of functional Itô’s lemma for semimartingales with an application

Author

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  • Levental, Shlomo
  • Schroder, Mark
  • Sinha, Sumit

Abstract

The Itô formula was extended recently by Dupire (2009) to functionals of paths of continuous semimartingales, and by Cont and Fournié (2010a) to functionals of paths of RCLL semimartingales. In contrast to the traditional formula that applies to functions of the current value of a process, these extensions apply to functionals of the history of a process. By modifying Dupire’s setup we develop new proofs for both the continuous case and the more general RCLL case that are much simpler. We also examine an application to optimal control.

Suggested Citation

  • Levental, Shlomo & Schroder, Mark & Sinha, Sumit, 2013. "A simple proof of functional Itô’s lemma for semimartingales with an application," Statistics & Probability Letters, Elsevier, vol. 83(9), pages 2019-2026.
    • Handle: RePEc:eee:stapro:v:83:y:2013:i:9:p:2019-2026
    DOI: 10.1016/j.spl.2013.05.010
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    Cited by:

    1. Siu, Tak Kuen, 2016. "A functional Itô’s calculus approach to convex risk measures with jump diffusion," European Journal of Operational Research, Elsevier, vol. 250(3), pages 874-883.
    2. Kromer, E. & Overbeck, L. & Röder, J.A.L., 2015. "Feynman–Kac for functional jump diffusions with an application to Credit Value Adjustment," Statistics & Probability Letters, Elsevier, vol. 105(C), pages 120-129.

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