We propose an approach to the valuation of payoffs in general semimartingale models of financial markets where prices are nonnegative. Each asset price can hit 0; we only exclude that this ever happens simultaneously for all assets. We start from two simple, economically motivated axioms, namely...

For a large financial market (which is a sequence of usual, “small” financial markets), we introduce and study a concept of no asymptotic arbitrage (of the first kind) which is invariant under discounting. We give two dual characterisations of this property in terms of (1) martingale-like...

In general multi-asset models of financial markets, the classic no-arbitrage concepts NFLVR and NUPBR have the serious shortcoming that they depend crucially on the way prices are discounted. To avoid this economically unnatural behaviour, we introduce a new way of defining “absence of...

As a corollary to Delbaen and Schachermayer’s fundamental theorem of asset pricing (Delbaen in Math. Ann. 300:463–520, <CitationRef CitationID="CR5">1994</CitationRef>; Stoch. Stoch. Rep. 53:213–226, <CitationRef CitationID="CR6">1995</CitationRef>; Math. Ann. 312:215–250, <CitationRef CitationID="CR7">1998</CitationRef>), we prove, in a general finite-dimensional semimartingale setting, that the no unbounded profit...</citationref></citationref></citationref>

The well-known absence-of-arbitrage condition NFLVR from the fundamental theorem of asset pricing splits into two conditions, called NA and NUPBR. We give a literature overview of several equivalent reformulations of NUPBR; these include existence of a growth-optimal portfolio, existence of the...