A Robust Fundamental Theorem of Asset Pricing with Discrete Martingale Measures

Abstract

The classical version of the Fundamental Theorem of Asset Pricing requires that zero-sets of the real-world probability measure P are known. We chose a different route and start from a possibly non-dominated set of probability measures P representing uncertainty about the zero-sets of the real world measure. Since the concept of equivalence of measures becomes meaningless under such a framework, we use the notion of P-full support, which is a condition on the support of a martingale measure Q. We derive a version of the Fundamental Theorem of Asset Pricing and find that no-arbitrage, in our context, is equivalent to the existence of a discrete martingale measure.