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On Itô’s formula for semimartingales with jumps and non-C2 functions

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  • Eisenberg, Julia
  • Krühner, Paul

Abstract

This paper considers a variant of Itô’s formula for discontinuous semimartingales and non-C2 functions. This result is particularly helpful for insurance control problems with Markov-modulated components. An example of a dividend barrier strategy for a Brownian risk model with Markov-switching illustrates the result.

Suggested Citation

  • Eisenberg, Julia & Krühner, Paul, 2022. "On Itô’s formula for semimartingales with jumps and non-C2 functions," Statistics & Probability Letters, Elsevier, vol. 184(C).
    • Handle: RePEc:eee:stapro:v:184:y:2022:i:c:s0167715222000049
    DOI: 10.1016/j.spl.2022.109369
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    References listed on IDEAS

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    1. Brinker, Leonie Violetta & Eisenberg, Julia, 2021. "Dividend optimisation: A behaviouristic approach," Insurance: Mathematics and Economics, Elsevier, vol. 101(PB), pages 202-224.
    2. Eisenberg, Julia & Krühner, Paul, 2018. "The impact of negative interest rates on optimal capital injections," Insurance: Mathematics and Economics, Elsevier, vol. 82(C), pages 1-10.
    3. Asmussen, Soren & Taksar, Michael, 1997. "Controlled diffusion models for optimal dividend pay-out," Insurance: Mathematics and Economics, Elsevier, vol. 20(1), pages 1-15, June.
    4. Jacka, Saul D. & Ocejo, Adriana, 2018. "On the regularity of American options with regime-switching uncertainty," Stochastic Processes and their Applications, Elsevier, vol. 128(3), pages 803-818.
    5. Zhengjun Jiang & Martijn Pistorius, 2012. "Optimal dividend distribution under Markov regime switching," Finance and Stochastics, Springer, vol. 16(3), pages 449-476, July.
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    Cited by:

    1. Ren'e Aid & Matteo Basei & Giorgio Ferrari, 2023. "A Stationary Mean-Field Equilibrium Model of Irreversible Investment in a Two-Regime Economy," Papers 2305.00541, arXiv.org.
    2. Aïd, René & Basei, Matteo & Ferrari, Giorgio, 2023. "A Stationary Mean-Field Equilibrium Model of Irreversible Investment in a Two-Regime Economy," Center for Mathematical Economics Working Papers 679, Center for Mathematical Economics, Bielefeld University.

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