Making no-arbitrage discounting-invariant: A new FTAP version beyond NFLVR and NUPBR

<p style='text-indent:20px;'>What is absence of arbitrage for non-discounted prices? How can one define this so that it does not change meaning if decides to discount after all?</p><p style='text-indent:20px;'>The answer both questions a new discounting-invariant no-arbitrage concept. As in earlier work, we as the zero strategy or some basic strategies being <i>maximal</i>. The key novelty maximality defined terms <i>share</i> holdings instead <i>value</i>. This allows us generalise NFLVR, by dynamic share efficienc, and NUPBR, viability. These concepts are same discounted undiscounted prices, they be used general models under minimal assumptions on asset prices. We establish corresponding versions FTAP, i.e., dual characterisations martingale properties. expects, "properly anticipated prices fluctuate randomly", but with an <i>endogenous</i> discounting process which cannot chosen priori. An example <i>N</i> geometric Brownian motions illustrates our results.</p>