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It\^o's formula for finite variation L\'evy processes: The case of non-smooth functions

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  • Ramin Okhrati
  • Uwe Schmock

Abstract

Extending It\^o's formula to non-smooth functions is important both in theory and applications. One of the fairly general extensions of the formula, known as Meyer-It\^o, applies to one dimensional semimartingales and convex functions. There are also satisfactory generalizations of It\^o's formula for diffusion processes where the Meyer-It\^o assumptions are weakened even further. We study a version of It\^o's formula for multi-dimensional finite variation L\'evy processes assuming that the underlying function is continuous and admits weak derivatives. We also discuss some applications of this extension, particularly in finance.

Suggested Citation

  • Ramin Okhrati & Uwe Schmock, 2015. "It\^o's formula for finite variation L\'evy processes: The case of non-smooth functions," Papers 1507.00294, arXiv.org.
    • Handle: RePEc:arx:papers:1507.00294
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    References listed on IDEAS

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    1. Rong, Situ, 1997. "On solutions of backward stochastic differential equations with jumps and applications," Stochastic Processes and their Applications, Elsevier, vol. 66(2), pages 209-236, March.
    2. Bardina, Xavier & Jolis, Maria, 1997. "An extension of Ito's formula for elliptic diffusion processes," Stochastic Processes and their Applications, Elsevier, vol. 69(1), pages 83-109, July.
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    Cited by:

    1. Kyriakos Georgiou & Athanasios N. Yannacopoulos, 2023. "Probability of Default modelling with L\'evy-driven Ornstein-Uhlenbeck processes and applications in credit risk under the IFRS 9," Papers 2309.12384, arXiv.org.

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