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I have a question about the following paper by Beatrice Acciaio, Mathias Beiglböck, Friedrich Penkner, Walter Schachermayer. At the very beginning of the paper, on page 3, there are two definitions which are not clear to me.

  1. Why can we assume W.l.o.g. that the prices of the options are $0$?
  2. In the definition of admissible measures, equation (1.1), how is this definition motivated? Especially why $$\int_{\mathbb{R}^T_+}\varphi_i(x)d\pi(x)\le 0, \forall i\in I $$

Thanks in advance

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