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Optional Decomposition for continuous semimartingales under arbitrary filtrations

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  • Ioannis Karatzas
  • Constantinos Kardaras

Abstract

We present an elementary treatment of the Optional Decomposition Theorem for continuous semimartingales and general filtrations. This treatment does not assume the existence of equivalent local martingale measure(s), only that of strictly positive local martingale deflator(s).

Suggested Citation

  • Ioannis Karatzas & Constantinos Kardaras, 2015. "Optional Decomposition for continuous semimartingales under arbitrary filtrations," Papers 1501.04274, arXiv.org, revised Feb 2015.
    • Handle: RePEc:arx:papers:1501.04274
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    Cited by:

    1. Erhan Bayraktar & Donghan Kim & Abhishek Tilva, 2024. "Arbitrage theory in a market of stochastic dimension," Mathematical Finance, Wiley Blackwell, vol. 34(3), pages 847-895, July.
    2. Berkaoui, Abdelkarem, 2023. "On the optional and orthogonal decompositions of supermartingales and applications," Statistics & Probability Letters, Elsevier, vol. 199(C).
    3. Oleksii Mostovyi, 2020. "Stability of the indirect utility process," Papers 2002.09445, arXiv.org.

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