A Robust Fundamental Theorem of Asset Pricing with Discrete Martingale Measures
25 Pages Posted: 9 Oct 2014 Last revised: 19 May 2015
Date Written: May 8, 2015
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.
Keywords: Fundamental Theorem of Asset Pricing, uncertainty, multiple prior, P-arbitrage.
JEL Classification: G12, D53
Suggested Citation: Suggested Citation