Generalized supermartingale deflators under limited information

TL;DR

This paper explores financial markets with limited information, establishing a link between market viability and the existence of a positive deflator that ensures wealth processes behave as generalized supermartingales.

Contribution

It introduces a novel framework for wealth processes based on economic properties rather than stochastic integrals, extending supermartingale deflator theory to limited information settings.

Findings

Equivalence between bounded terminal wealth and market viability

Existence of a positive deflator with generalized supermartingale property

Framework applicable to markets with limited information

Abstract

We undertake a study of markets from the perspective of a financial agent with limited access to information. The set of wealth processes available to the agent is structured with reasonable economic properties, instead of the usual practice of taking it to consist of stochastic integrals against a semimartingale integrator. We obtain the equivalence of the boundedness in probability of the set of terminal wealth outcomes (which in turn is equivalent to the weak market viability condition of absence of arbitrage of the first kind) with the existence of at least one strictly positive deflator that makes the deflated wealth processes have a generalized supermartingale property.