Uncertainty and absence of arbitrage opportunity

TL;DR

This paper demonstrates that the absence of arbitrage opportunities in financial markets can be viewed as a specific case of uncertainty within decision systems, linking economic theory with decision-making principles.

Contribution

It introduces a novel perspective by connecting arbitrage absence to uncertainty, based on the principle of internal coherence, extending the theoretical understanding of financial market conditions.

Findings

Absence of arbitrage is a special case of uncertainty.

The framework is based on the Arrow-Debreu model.

Uncertainty is defined through Allais's principle of internal coherence.

Abstract

It is shown that absence of arbitrage opportunity in financial markets is a particular case of existence of uncertainty in decision system. Absence of arbitrage opportunity is considered in the sense of the Arrow-Debreu model of financial market with a riskless asset, while uncertainty (or ambiguity) is defined on the basis of the principle of internal coherence of M. Allais.