Drift operator in a viable expansion of information flow

TL;DR

This paper investigates conditions under which the viability of a financial market model is preserved when the information flow is expanded, focusing on the role of the drift operator in this context.

Contribution

It provides a necessary and sufficient condition for market viability preservation under information flow enlargement, assuming the martingale representation property.

Findings

Established a criterion for viability preservation during information flow enlargement.

Demonstrated the importance of the drift operator in maintaining market viability.

Extended understanding of market stability under increased information flow.

Abstract

A triplet $(\mathbb{P},\mathbb{F},S)$ of a probability measure $\mathbb{P}$, of an information flow $\mathbb{F}=(\mathcal{F}_t)_{t\in\mathbb{R}_+}$, and of an $\mathbb{F}$ adapted asset process $S$, is a financial market model, only if it is viable. In this paper we are concerned with the preservation of the market viability, when the information flow $\mathbb{F}$ is replaced by a bigger one $\mathbb{G}=(\mathcal{G}_t)_{t\geq 0}$ with $\mathcal{G}_t\supset\mathcal{F}_t$. Under the assumption of martingale representation property in $(\mathbb{P},\mathbb{F})$, we prove a necessary and sufficient condition for all viable market in $\mathbb{F}$ to remain viable in $\mathbb{G}$.