Pricing without equivalent martingale measures under complete and incomplete observation

Traditional arbitrage pricing theory is based on martingale measures. Recent studies show that some form of arbitrage may exist in real markets implying that then there does not exist an equivalent martingale measure and so the question arises: what can one do with pricing and hedging in this situation? We mention here two approaches to this effect that have appeared in the literature, namely the ``Fernholz-Karatzas" approach and Platen's "Benchmark approach" and discuss their relationships both in models where all relevant quantities are fully observable as well as in models where this is not the case and, furthermore, not all observables are also investment instruments.

[The talk is based on joint work with former student Giorgia Galesso]