Model Uncertainty: A Reverse Approach

Abstract

In robust finance, Knightian uncertainty is often captured by sets of probability measures on the future states of the world. If these measures are nondominated, this usually comes at the cost of losing tractability, and advanced functional-analytic tools are often not available anymore. This tends to be mitigated by ad hoc assumptions that guarantee a certain degree of tractability, for instance concerning the aggregation of consistent random variables. The present paper instead investigates from a reverse perspective what implications the validity of certain functional-analytic tools has. In this vein, we categorise the Kreps-Yan property, robust variants of the Brannath-Schachermayer Bipolar Theorem and the Grothendieck Lemma, and uncertain volatility models. By doing so, we also uncover connections to robust statistics.