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1 results

  • No arbitrage and multiplicative special semimartingales

  • Part of
  • Eckhard Platen, Stefan Tappe
  • Journal:
    Advances in Applied Probability / Volume 55 / Issue 3 / September 2023
    Published online by Cambridge University Press:
    09 June 2023, pp. 1033-1074
    Print publication:
    September 2023
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  • Consider a financial market with nonnegative semimartingales which does not need to have a numéraire. 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.