Viability and Arbitrage under Knightian Uncertainty

TL;DR

This paper explores the implications of Knightian Uncertainty in financial markets by developing a model without probabilistic assumptions, establishing a link between market viability and arbitrage absence, and modifying the Fundamental Theorem of Asset Pricing.

Contribution

It introduces a probabilistic-free model based on a common order, connecting market viability with arbitrage and adapting core financial theorems under uncertainty.

Findings

Market viability is equivalent to no arbitrage under Knightian Uncertainty.

A modified Fundamental Theorem of Asset Pricing is derived using sublinear pricing measures.

Different forms of the Efficient Market Hypothesis relate to assumptions on the common order.

Abstract

We reconsider the microeconomic foundations of financial economics. Motivated by the importance of Knightian Uncertainty in markets, we present a model that does not carry any probabilistic structure ex ante, yet is based on a common order. We derive the fundamental equivalence of economic viability of asset prices and absence of arbitrage. We also obtain a modified version of the Fundamental Theorem of Asset Pricing using the notion of sublinear pricing measures. Different versions of the Efficient Market Hypothesis are related to the assumptions one is willing to impose on the common order.