On the semimartingale property of discounted asset-price processes

TL;DR

This paper proves that in a realistic financial market model, the absence of arbitrages of the first kind implies that discounted asset prices must be semimartingales, even without assuming this property initially.

Contribution

It establishes that minimal market viability conditions ensure the semimartingale property of asset prices without prior assumptions.

Findings

Discounted asset prices are semimartingales under no arbitrage of the first kind.

The result extends to cases involving supermartingale deflators instead of equivalent martingale measures.

Minimal assumptions suffice to guarantee the semimartingale property in realistic market models.

Abstract

A financial market model where agents trade using realistic combinations of buy-and-hold strategies is considered. Minimal assumptions are made on the discounted asset-price process - in particular, the semimartingale property is not assumed. Via a natural market viability assumption, namely, absence of arbitrages of the first kind, we establish that discounted asset-prices have to be semimartingales. In a slightly more specialized case, we extend the previous result in a weakened version of the Fundamental Theorem of Asset Pricing that involves strictly positive supermartingale deflators rather than Equivalent Martingale Measures.