Market viability via absence of arbitrage of the first kind

TL;DR

This paper establishes a fundamental link in financial mathematics by showing that the absence of arbitrage of the first kind in a semimartingale market is equivalent to the existence of a local martingale deflator, ensuring market viability.

Contribution

It proves the equivalence between a weak no-arbitrage condition and the existence of a local martingale deflator in semimartingale models.

Findings

Absence of arbitrage of the first kind implies existence of a local martingale deflator.

The equivalence provides a characterization of market viability.

The result applies to general semimartingale market models.

Abstract

In a semimartingale financial market model, it is shown that there is equivalence between absence of arbitrage of the first kind (a weak viability condition) and the existence of a strictly positive process that acts as a local martingale deflator on nonnegative wealth processes.