We provide a general framework to study viability and arbitrage in models for financial markets. Viability is intended as the existence of a preference relation with the following properties: It is consistent with a set of preferences representing all the plausible agents trading in the market; An agent with such a preference is in equilibrium, namely, he or she prefers to stay at the initial endowment respect to trade. We extend the original framework of Kreps ('79) and Harrison-Kreps ('79) to accommodate for Knightian Uncertainty: preferences of plausible agents are not necessarily determined by a single probability measure. The relations between arbitrage, viability, and existence of (non-)linear pricing rules are investigated.
This is a joint work with Frank Riedel and Mete Soner.[-]

For large financial markets as introduced in Kramkov and Kabanov 94, there are several existing absence-of-arbitrage conditions in the literature. They all have in common that they depend in a crucial way on the discounting factor. We introduce a new concept, generalizing NAA1 (K&K 94) and NAA (Rokhlin 08), which is invariant with respect to discounting. We derive a dual characterization by a contiguity property (FTAP).We investigate connections to the in finite time horizon framework (as for example in Karatzas and Kardaras 07) and illustrate negative result by counterexamples. Based on joint work with M. Schweizer.[-]