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On linear stochastic equations of optional semimartingales and their applications

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  • Abdelghani, Mohamed N.
  • Melnikov, Alexander V.

Abstract

Elements of the stochastic calculus of optional semimartingales are presented. A solution of the nonhomogeneous and general linear stochastic equations is given in this framework. Also, the Gronwall inequality is derived. Furthermore, a theory of martingale transforms and examples of applications to mathematical finance are presented.

Suggested Citation

  • Abdelghani, Mohamed N. & Melnikov, Alexander V., 2017. "On linear stochastic equations of optional semimartingales and their applications," Statistics & Probability Letters, Elsevier, vol. 125(C), pages 207-214.
    • Handle: RePEc:eee:stapro:v:125:y:2017:i:c:p:207-214
    DOI: 10.1016/j.spl.2017.02.014
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    References listed on IDEAS

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    1. Christoph Czichowsky & Walter Schachermayer, 2014. "Duality Theory for Portfolio Optimisation under Transaction Costs," Papers 1408.5989, arXiv.org.
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    Cited by:

    1. Hilbert, Astrid & Jarni, Imane & Ouknine, Youssef, 2020. "On reflected stochastic differential equations driven by regulated semimartingales," Statistics & Probability Letters, Elsevier, vol. 167(C).
    2. Mohamed N. Abdelghani & Alexander V. Melnikov, 2017. "Optional Defaultable Markets," Risks, MDPI, vol. 5(4), pages 1-21, October.
    3. Imane Jarni & Youssef Ouknine, 2021. "On Reflection with Two-Sided Jumps," Journal of Theoretical Probability, Springer, vol. 34(4), pages 1811-1830, December.

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