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No arbitrage and multiplicative special semimartingales

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  • Eckhard Platen
  • Stefan Tappe

Abstract

Consider a financial market with nonnegative semimartingales which does not need to have a num\'{e}raire. We are interested in the absence of arbitrage in the sense that no self-financing portfolio gives rise to arbitrage opportunities, where we are allowed to add a savings account to the market. We will prove that in this sense the market is free of arbitrage if and only if there exists an equivalent local martingale deflator which is a multiplicative special semimartingale. In this case, the additional savings account relates to the finite variation part of the multiplicative decomposition of the deflator.

Suggested Citation

  • Eckhard Platen & Stefan Tappe, 2020. "No arbitrage and multiplicative special semimartingales," Papers 2005.05575, arXiv.org, revised Sep 2022.
    • Handle: RePEc:arx:papers:2005.05575
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    References listed on IDEAS

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    Cited by:

    1. Eckhard Platen & Stefan Tappe, 2020. "Exploiting arbitrage requires short selling," Papers 2011.12523, arXiv.org, revised Sep 2022.

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