We study general undiscounted asset price processes, which are only assumed to be non- negative, adapted and RCLL (but not a priori semimartingales). Traders are allowed to use simple (piecewise constant) strategies. We prove that under a discounting-invariant condition of absence of arbitrage,...

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>

Let X be a continuous adapted process for which there exists an equivalent local martingale measure (ELMM). The minimal martingale measure P is the unique ELMM for X with the property that local P-martingales strongly orthogonal to the P-martingale part of X are also local P-martingales. We...

We use probabilistic methods to study classical solutions for systems of interacting semilinear parabolic partial differential equations. In a modeling framework for a financial market with interacting Ito and point processes, such PDEs are shown to provide a natural description for the solution...